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
Autor*in: |
Win, Aung Naing [verfasserIn] |
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E-Artikel |
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Englisch |
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2022transfer abstract |
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Umfang: |
11 |
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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.] |
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Übergeordnetes Werk: |
volume:193 ; year:2022 ; pages:556-566 ; extent:11 |
Links: |
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DOI / URN: |
10.1016/j.matcom.2021.10.031 |
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ELV056069693 |
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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. | ||
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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 |
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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 |
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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 |
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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 |
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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 |
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Numerical method based on fiber bundle for solving Lyapunov matrix equation |
author_sort |
Win, Aung Naing |
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Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model |
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Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model |
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Win, Aung Naing |
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Elektronische Aufsätze |
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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. |
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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 |
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up_date |
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