Numerical method based on fiber bundle for solving Lyapunov matrix equation
In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the s...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Win, Aung Naing [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2022transfer abstract |
|---|
| Schlagwörter: |
|---|
| Umfang: |
11 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model - Hendawy, Hanan ELSEVIER, 2022, transactions of IMACS, Amsterdam [u.a.] |
|---|---|
| Übergeordnetes Werk: |
volume:193 ; year:2022 ; pages:556-566 ; extent:11 |
| Links: |
|---|
| DOI / URN: |
10.1016/j.matcom.2021.10.031 |
|---|
| Katalog-ID: |
ELV056069693 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | ELV056069693 | ||
| 003 | DE-627 | ||
| 005 | 20230626042655.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 220105s2022 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1016/j.matcom.2021.10.031 |2 doi | |
| 028 | 5 | 2 | |a /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001609.pica |
| 035 | |a (DE-627)ELV056069693 | ||
| 035 | |a (ELSEVIER)S0378-4754(21)00394-3 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 610 |q VZ |
| 084 | |a 44.40 |2 bkl | ||
| 100 | 1 | |a Win, Aung Naing |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Numerical method based on fiber bundle for solving Lyapunov matrix equation |
| 264 | 1 | |c 2022transfer abstract | |
| 300 | |a 11 | ||
| 336 | |a nicht spezifiziert |b zzz |2 rdacontent | ||
| 337 | |a nicht spezifiziert |b z |2 rdamedia | ||
| 338 | |a nicht spezifiziert |b zu |2 rdacarrier | ||
| 520 | |a In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. | ||
| 520 | |a In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. | ||
| 650 | 7 | |a Positive definite Hermitian matrix |2 Elsevier | |
| 650 | 7 | |a Riemannian gradient |2 Elsevier | |
| 650 | 7 | |a Stability |2 Elsevier | |
| 650 | 7 | |a Geodesic distance |2 Elsevier | |
| 650 | 7 | |a Lyapunov equation |2 Elsevier | |
| 700 | 1 | |a Li, Mingming |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier Science |a Hendawy, Hanan ELSEVIER |t Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model |d 2022 |d transactions of IMACS |g Amsterdam [u.a.] |w (DE-627)ELV009822585 |
| 773 | 1 | 8 | |g volume:193 |g year:2022 |g pages:556-566 |g extent:11 |
| 856 | 4 | 0 | |u https://doi.org/10.1016/j.matcom.2021.10.031 |3 Volltext |
| 912 | |a GBV_USEFLAG_U | ||
| 912 | |a GBV_ELV | ||
| 912 | |a SYSFLAG_U | ||
| 912 | |a SSG-OLC-PHA | ||
| 912 | |a SSG-OPC-PHA | ||
| 936 | b | k | |a 44.40 |j Pharmazie |j Pharmazeutika |q VZ |
| 951 | |a AR | ||
| 952 | |d 193 |j 2022 |h 556-566 |g 11 | ||
| author_variant |
a n w an anw |
|---|---|
| matchkey_str |
winaungnainglimingming:2022----:ueiamtobsdniebnlfrovnlau |
| hierarchy_sort_str |
2022transfer abstract |
| bklnumber |
44.40 |
| publishDate |
2022 |
| allfields |
10.1016/j.matcom.2021.10.031 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001609.pica (DE-627)ELV056069693 (ELSEVIER)S0378-4754(21)00394-3 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Win, Aung Naing verfasserin aut Numerical method based on fiber bundle for solving Lyapunov matrix equation 2022transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. Positive definite Hermitian matrix Elsevier Riemannian gradient Elsevier Stability Elsevier Geodesic distance Elsevier Lyapunov equation Elsevier Li, Mingming oth Enthalten in Elsevier Science Hendawy, Hanan ELSEVIER Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model 2022 transactions of IMACS Amsterdam [u.a.] (DE-627)ELV009822585 volume:193 year:2022 pages:556-566 extent:11 https://doi.org/10.1016/j.matcom.2021.10.031 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 193 2022 556-566 11 |
| spelling |
10.1016/j.matcom.2021.10.031 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001609.pica (DE-627)ELV056069693 (ELSEVIER)S0378-4754(21)00394-3 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Win, Aung Naing verfasserin aut Numerical method based on fiber bundle for solving Lyapunov matrix equation 2022transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. Positive definite Hermitian matrix Elsevier Riemannian gradient Elsevier Stability Elsevier Geodesic distance Elsevier Lyapunov equation Elsevier Li, Mingming oth Enthalten in Elsevier Science Hendawy, Hanan ELSEVIER Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model 2022 transactions of IMACS Amsterdam [u.a.] (DE-627)ELV009822585 volume:193 year:2022 pages:556-566 extent:11 https://doi.org/10.1016/j.matcom.2021.10.031 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 193 2022 556-566 11 |
| allfields_unstemmed |
10.1016/j.matcom.2021.10.031 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001609.pica (DE-627)ELV056069693 (ELSEVIER)S0378-4754(21)00394-3 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Win, Aung Naing verfasserin aut Numerical method based on fiber bundle for solving Lyapunov matrix equation 2022transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. Positive definite Hermitian matrix Elsevier Riemannian gradient Elsevier Stability Elsevier Geodesic distance Elsevier Lyapunov equation Elsevier Li, Mingming oth Enthalten in Elsevier Science Hendawy, Hanan ELSEVIER Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model 2022 transactions of IMACS Amsterdam [u.a.] (DE-627)ELV009822585 volume:193 year:2022 pages:556-566 extent:11 https://doi.org/10.1016/j.matcom.2021.10.031 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 193 2022 556-566 11 |
| allfieldsGer |
10.1016/j.matcom.2021.10.031 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001609.pica (DE-627)ELV056069693 (ELSEVIER)S0378-4754(21)00394-3 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Win, Aung Naing verfasserin aut Numerical method based on fiber bundle for solving Lyapunov matrix equation 2022transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. Positive definite Hermitian matrix Elsevier Riemannian gradient Elsevier Stability Elsevier Geodesic distance Elsevier Lyapunov equation Elsevier Li, Mingming oth Enthalten in Elsevier Science Hendawy, Hanan ELSEVIER Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model 2022 transactions of IMACS Amsterdam [u.a.] (DE-627)ELV009822585 volume:193 year:2022 pages:556-566 extent:11 https://doi.org/10.1016/j.matcom.2021.10.031 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 193 2022 556-566 11 |
| allfieldsSound |
10.1016/j.matcom.2021.10.031 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001609.pica (DE-627)ELV056069693 (ELSEVIER)S0378-4754(21)00394-3 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Win, Aung Naing verfasserin aut Numerical method based on fiber bundle for solving Lyapunov matrix equation 2022transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. Positive definite Hermitian matrix Elsevier Riemannian gradient Elsevier Stability Elsevier Geodesic distance Elsevier Lyapunov equation Elsevier Li, Mingming oth Enthalten in Elsevier Science Hendawy, Hanan ELSEVIER Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model 2022 transactions of IMACS Amsterdam [u.a.] (DE-627)ELV009822585 volume:193 year:2022 pages:556-566 extent:11 https://doi.org/10.1016/j.matcom.2021.10.031 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 193 2022 556-566 11 |
| language |
English |
| source |
Enthalten in Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model Amsterdam [u.a.] volume:193 year:2022 pages:556-566 extent:11 |
| sourceStr |
Enthalten in Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model Amsterdam [u.a.] volume:193 year:2022 pages:556-566 extent:11 |
| format_phy_str_mv |
Article |
| bklname |
Pharmazie Pharmazeutika |
| institution |
findex.gbv.de |
| topic_facet |
Positive definite Hermitian matrix Riemannian gradient Stability Geodesic distance Lyapunov equation |
| dewey-raw |
610 |
| isfreeaccess_bool |
false |
| container_title |
Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model |
| authorswithroles_txt_mv |
Win, Aung Naing @@aut@@ Li, Mingming @@oth@@ |
| publishDateDaySort_date |
2022-01-01T00:00:00Z |
| hierarchy_top_id |
ELV009822585 |
| dewey-sort |
3610 |
| id |
ELV056069693 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV056069693</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230626042655.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220105s2022 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.matcom.2021.10.031</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">/cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001609.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV056069693</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0378-4754(21)00394-3</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">610</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44.40</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Win, Aung Naing</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Numerical method based on fiber bundle for solving Lyapunov matrix equation</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022transfer abstract</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">11</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Positive definite Hermitian matrix</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Riemannian gradient</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stability</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geodesic distance</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Lyapunov equation</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Li, Mingming</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier Science</subfield><subfield code="a">Hendawy, Hanan ELSEVIER</subfield><subfield code="t">Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model</subfield><subfield code="d">2022</subfield><subfield code="d">transactions of IMACS</subfield><subfield code="g">Amsterdam [u.a.]</subfield><subfield code="w">(DE-627)ELV009822585</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:193</subfield><subfield code="g">year:2022</subfield><subfield code="g">pages:556-566</subfield><subfield code="g">extent:11</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.matcom.2021.10.031</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-PHA</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">44.40</subfield><subfield code="j">Pharmazie</subfield><subfield code="j">Pharmazeutika</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">193</subfield><subfield code="j">2022</subfield><subfield code="h">556-566</subfield><subfield code="g">11</subfield></datafield></record></collection>
|
| author |
Win, Aung Naing |
| spellingShingle |
Win, Aung Naing ddc 610 bkl 44.40 Elsevier Positive definite Hermitian matrix Elsevier Riemannian gradient Elsevier Stability Elsevier Geodesic distance Elsevier Lyapunov equation Numerical method based on fiber bundle for solving Lyapunov matrix equation |
| authorStr |
Win, Aung Naing |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)ELV009822585 |
| format |
electronic Article |
| dewey-ones |
610 - Medicine & health |
| delete_txt_mv |
keep |
| author_role |
aut |
| collection |
elsevier |
| remote_str |
true |
| illustrated |
Not Illustrated |
| topic_title |
610 VZ 44.40 bkl Numerical method based on fiber bundle for solving Lyapunov matrix equation Positive definite Hermitian matrix Elsevier Riemannian gradient Elsevier Stability Elsevier Geodesic distance Elsevier Lyapunov equation Elsevier |
| topic |
ddc 610 bkl 44.40 Elsevier Positive definite Hermitian matrix Elsevier Riemannian gradient Elsevier Stability Elsevier Geodesic distance Elsevier Lyapunov equation |
| topic_unstemmed |
ddc 610 bkl 44.40 Elsevier Positive definite Hermitian matrix Elsevier Riemannian gradient Elsevier Stability Elsevier Geodesic distance Elsevier Lyapunov equation |
| topic_browse |
ddc 610 bkl 44.40 Elsevier Positive definite Hermitian matrix Elsevier Riemannian gradient Elsevier Stability Elsevier Geodesic distance Elsevier Lyapunov equation |
| format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
zu |
| author2_variant |
m l ml |
| hierarchy_parent_title |
Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model |
| hierarchy_parent_id |
ELV009822585 |
| dewey-tens |
610 - Medicine & health |
| hierarchy_top_title |
Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)ELV009822585 |
| title |
Numerical method based on fiber bundle for solving Lyapunov matrix equation |
| ctrlnum |
(DE-627)ELV056069693 (ELSEVIER)S0378-4754(21)00394-3 |
| title_full |
Numerical method based on fiber bundle for solving Lyapunov matrix equation |
| author_sort |
Win, Aung Naing |
| journal |
Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model |
| journalStr |
Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
600 - Technology |
| recordtype |
marc |
| publishDateSort |
2022 |
| contenttype_str_mv |
zzz |
| container_start_page |
556 |
| author_browse |
Win, Aung Naing |
| container_volume |
193 |
| physical |
11 |
| class |
610 VZ 44.40 bkl |
| format_se |
Elektronische Aufsätze |
| author-letter |
Win, Aung Naing |
| doi_str_mv |
10.1016/j.matcom.2021.10.031 |
| dewey-full |
610 |
| title_sort |
numerical method based on fiber bundle for solving lyapunov matrix equation |
| title_auth |
Numerical method based on fiber bundle for solving Lyapunov matrix equation |
| abstract |
In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. |
| abstractGer |
In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. |
| abstract_unstemmed |
In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA. |
| collection_details |
GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA |
| title_short |
Numerical method based on fiber bundle for solving Lyapunov matrix equation |
| url |
https://doi.org/10.1016/j.matcom.2021.10.031 |
| remote_bool |
true |
| author2 |
Li, Mingming |
| author2Str |
Li, Mingming |
| ppnlink |
ELV009822585 |
| mediatype_str_mv |
z |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| author2_role |
oth |
| doi_str |
10.1016/j.matcom.2021.10.031 |
| up_date |
2024-07-06T19:20:52.137Z |
| _version_ |
1803858636584255488 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV056069693</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230626042655.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220105s2022 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.matcom.2021.10.031</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">/cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001609.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV056069693</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0378-4754(21)00394-3</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">610</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44.40</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Win, Aung Naing</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Numerical method based on fiber bundle for solving Lyapunov matrix equation</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022transfer abstract</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">11</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Positive definite Hermitian matrix</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Riemannian gradient</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stability</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geodesic distance</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Lyapunov equation</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Li, Mingming</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier Science</subfield><subfield code="a">Hendawy, Hanan ELSEVIER</subfield><subfield code="t">Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model</subfield><subfield code="d">2022</subfield><subfield code="d">transactions of IMACS</subfield><subfield code="g">Amsterdam [u.a.]</subfield><subfield code="w">(DE-627)ELV009822585</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:193</subfield><subfield code="g">year:2022</subfield><subfield code="g">pages:556-566</subfield><subfield code="g">extent:11</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.matcom.2021.10.031</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-PHA</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">44.40</subfield><subfield code="j">Pharmazie</subfield><subfield code="j">Pharmazeutika</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">193</subfield><subfield code="j">2022</subfield><subfield code="h">556-566</subfield><subfield code="g">11</subfield></datafield></record></collection>
|
| score |
7.4002304 |