New algorithm for computing the Hermite interpolation polynomial

Abstract Let x0, x1,⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xi ≠ xj, for i ≠ j) and yi, k, for i = 0,1,⋯ , n, and k = 0 ,1 ,⋯ , ni, with ni ≥ 1, be given of real numbers, we know that there exists a unique polynomial pN − 1(x) of degree N − 1 where $N={\sum }_{i=0}^{n}(n_{i}+1)$, such...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Messaoudi, A. [verfasserIn] Sadaka, R. [verfasserIn] Sadok, H. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	Polynomial interpolation Hermite interpolation polynomials Schur complement Matrix Sylvester identity Recursive polynomial interpolation algorithm Matrix recursive interpolation algorithm

Übergeordnetes Werk:	Enthalten in: Numerical algorithms - Bussum : Baltzer, 1991, 77(2017), 4 vom: 31. Mai, Seite 1069-1092
Übergeordnetes Werk:	volume:77 ; year:2017 ; number:4 ; day:31 ; month:05 ; pages:1069-1092

Links:	Volltext

DOI / URN:	10.1007/s11075-017-0353-6

Katalog-ID:	SPR016430484

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245	1	0	\|a New algorithm for computing the Hermite interpolation polynomial
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520			\|a Abstract Let x0, x1,⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xi ≠ xj, for i ≠ j) and yi, k, for i = 0,1,⋯ , n, and k = 0 ,1 ,⋯ , ni, with ni ≥ 1, be given of real numbers, we know that there exists a unique polynomial pN − 1(x) of degree N − 1 where $N={\sum }_{i=0}^{n}(n_{i}+1)$, such that $p_{N-1}^{(k)}(x_{i})=y_{i,k}$, for i = 0,1,⋯ , n and k = 0,1,⋯ , ni. PN−1(x) is the Hermite interpolation polynomial for the set {(xi, yi, k), i = 0,1,⋯ , n, k = 0,1,⋯ , ni}. The polynomial pN−1(x) can be computed by using the Lagrange polynomials. This paper presents a new method for computing Hermite interpolation polynomials, for a particular case ni = 1. We will reformulate the Hermite interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Matrix Recursive Polynomial Interpolation Algorithm (MRPIA). Some properties of this algorithm will be studied and some examples will also be given.
650		4	\|a Polynomial interpolation \|7 (dpeaa)DE-He213
650		4	\|a Hermite interpolation polynomials \|7 (dpeaa)DE-He213
650		4	\|a Schur complement \|7 (dpeaa)DE-He213
650		4	\|a Matrix Sylvester identity \|7 (dpeaa)DE-He213
650		4	\|a Recursive polynomial interpolation algorithm \|7 (dpeaa)DE-He213
650		4	\|a Matrix recursive interpolation algorithm \|7 (dpeaa)DE-He213
700	1		\|a Sadaka, R. \|e verfasserin \|4 aut
700	1		\|a Sadok, H. \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Numerical algorithms \|d Bussum : Baltzer, 1991 \|g 77(2017), 4 vom: 31. Mai, Seite 1069-1092 \|w (DE-627)318468581 \|w (DE-600)2002650-X \|x 1572-9265 \|7 nnns
773	1	8	\|g volume:77 \|g year:2017 \|g number:4 \|g day:31 \|g month:05 \|g pages:1069-1092
856	4	0	\|u https://dx.doi.org/10.1007/s11075-017-0353-6 \|z lizenzpflichtig \|3 Volltext
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912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
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912			\|a GBV_ILN_2143
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952			\|d 77 \|j 2017 \|e 4 \|b 31 \|c 05 \|h 1069-1092

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author_variant	a m am r s rs h s hs
matchkey_str	article:15729265:2017----::eagrtmocmuighhrienepl
hierarchy_sort_str	2017
bklnumber	31.76
publishDate	2017
allfields	10.1007/s11075-017-0353-6 doi (DE-627)SPR016430484 (SPR)s11075-017-0353-6-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Messaoudi, A. verfasserin aut New algorithm for computing the Hermite interpolation polynomial 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let x0, x1,⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xi ≠ xj, for i ≠ j) and yi, k, for i = 0,1,⋯ , n, and k = 0 ,1 ,⋯ , ni, with ni ≥ 1, be given of real numbers, we know that there exists a unique polynomial pN − 1(x) of degree N − 1 where $N={\sum }_{i=0}^{n}(n_{i}+1)$, such that $p_{N-1}^{(k)}(x_{i})=y_{i,k}$, for i = 0,1,⋯ , n and k = 0,1,⋯ , ni. PN−1(x) is the Hermite interpolation polynomial for the set {(xi, yi, k), i = 0,1,⋯ , n, k = 0,1,⋯ , ni}. The polynomial pN−1(x) can be computed by using the Lagrange polynomials. This paper presents a new method for computing Hermite interpolation polynomials, for a particular case ni = 1. We will reformulate the Hermite interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Matrix Recursive Polynomial Interpolation Algorithm (MRPIA). Some properties of this algorithm will be studied and some examples will also be given. Polynomial interpolation (dpeaa)DE-He213 Hermite interpolation polynomials (dpeaa)DE-He213 Schur complement (dpeaa)DE-He213 Matrix Sylvester identity (dpeaa)DE-He213 Recursive polynomial interpolation algorithm (dpeaa)DE-He213 Matrix recursive interpolation algorithm (dpeaa)DE-He213 Sadaka, R. verfasserin aut Sadok, H. verfasserin aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 77(2017), 4 vom: 31. Mai, Seite 1069-1092 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:77 year:2017 number:4 day:31 month:05 pages:1069-1092 https://dx.doi.org/10.1007/s11075-017-0353-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 77 2017 4 31 05 1069-1092
spelling	10.1007/s11075-017-0353-6 doi (DE-627)SPR016430484 (SPR)s11075-017-0353-6-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Messaoudi, A. verfasserin aut New algorithm for computing the Hermite interpolation polynomial 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let x0, x1,⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xi ≠ xj, for i ≠ j) and yi, k, for i = 0,1,⋯ , n, and k = 0 ,1 ,⋯ , ni, with ni ≥ 1, be given of real numbers, we know that there exists a unique polynomial pN − 1(x) of degree N − 1 where $N={\sum }_{i=0}^{n}(n_{i}+1)$, such that $p_{N-1}^{(k)}(x_{i})=y_{i,k}$, for i = 0,1,⋯ , n and k = 0,1,⋯ , ni. PN−1(x) is the Hermite interpolation polynomial for the set {(xi, yi, k), i = 0,1,⋯ , n, k = 0,1,⋯ , ni}. The polynomial pN−1(x) can be computed by using the Lagrange polynomials. This paper presents a new method for computing Hermite interpolation polynomials, for a particular case ni = 1. We will reformulate the Hermite interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Matrix Recursive Polynomial Interpolation Algorithm (MRPIA). Some properties of this algorithm will be studied and some examples will also be given. Polynomial interpolation (dpeaa)DE-He213 Hermite interpolation polynomials (dpeaa)DE-He213 Schur complement (dpeaa)DE-He213 Matrix Sylvester identity (dpeaa)DE-He213 Recursive polynomial interpolation algorithm (dpeaa)DE-He213 Matrix recursive interpolation algorithm (dpeaa)DE-He213 Sadaka, R. verfasserin aut Sadok, H. verfasserin aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 77(2017), 4 vom: 31. Mai, Seite 1069-1092 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:77 year:2017 number:4 day:31 month:05 pages:1069-1092 https://dx.doi.org/10.1007/s11075-017-0353-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 77 2017 4 31 05 1069-1092
allfields_unstemmed	10.1007/s11075-017-0353-6 doi (DE-627)SPR016430484 (SPR)s11075-017-0353-6-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Messaoudi, A. verfasserin aut New algorithm for computing the Hermite interpolation polynomial 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let x0, x1,⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xi ≠ xj, for i ≠ j) and yi, k, for i = 0,1,⋯ , n, and k = 0 ,1 ,⋯ , ni, with ni ≥ 1, be given of real numbers, we know that there exists a unique polynomial pN − 1(x) of degree N − 1 where $N={\sum }_{i=0}^{n}(n_{i}+1)$, such that $p_{N-1}^{(k)}(x_{i})=y_{i,k}$, for i = 0,1,⋯ , n and k = 0,1,⋯ , ni. PN−1(x) is the Hermite interpolation polynomial for the set {(xi, yi, k), i = 0,1,⋯ , n, k = 0,1,⋯ , ni}. The polynomial pN−1(x) can be computed by using the Lagrange polynomials. This paper presents a new method for computing Hermite interpolation polynomials, for a particular case ni = 1. We will reformulate the Hermite interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Matrix Recursive Polynomial Interpolation Algorithm (MRPIA). Some properties of this algorithm will be studied and some examples will also be given. Polynomial interpolation (dpeaa)DE-He213 Hermite interpolation polynomials (dpeaa)DE-He213 Schur complement (dpeaa)DE-He213 Matrix Sylvester identity (dpeaa)DE-He213 Recursive polynomial interpolation algorithm (dpeaa)DE-He213 Matrix recursive interpolation algorithm (dpeaa)DE-He213 Sadaka, R. verfasserin aut Sadok, H. verfasserin aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 77(2017), 4 vom: 31. Mai, Seite 1069-1092 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:77 year:2017 number:4 day:31 month:05 pages:1069-1092 https://dx.doi.org/10.1007/s11075-017-0353-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 77 2017 4 31 05 1069-1092
allfieldsGer	10.1007/s11075-017-0353-6 doi (DE-627)SPR016430484 (SPR)s11075-017-0353-6-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Messaoudi, A. verfasserin aut New algorithm for computing the Hermite interpolation polynomial 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let x0, x1,⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xi ≠ xj, for i ≠ j) and yi, k, for i = 0,1,⋯ , n, and k = 0 ,1 ,⋯ , ni, with ni ≥ 1, be given of real numbers, we know that there exists a unique polynomial pN − 1(x) of degree N − 1 where $N={\sum }_{i=0}^{n}(n_{i}+1)$, such that $p_{N-1}^{(k)}(x_{i})=y_{i,k}$, for i = 0,1,⋯ , n and k = 0,1,⋯ , ni. PN−1(x) is the Hermite interpolation polynomial for the set {(xi, yi, k), i = 0,1,⋯ , n, k = 0,1,⋯ , ni}. The polynomial pN−1(x) can be computed by using the Lagrange polynomials. This paper presents a new method for computing Hermite interpolation polynomials, for a particular case ni = 1. We will reformulate the Hermite interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Matrix Recursive Polynomial Interpolation Algorithm (MRPIA). Some properties of this algorithm will be studied and some examples will also be given. Polynomial interpolation (dpeaa)DE-He213 Hermite interpolation polynomials (dpeaa)DE-He213 Schur complement (dpeaa)DE-He213 Matrix Sylvester identity (dpeaa)DE-He213 Recursive polynomial interpolation algorithm (dpeaa)DE-He213 Matrix recursive interpolation algorithm (dpeaa)DE-He213 Sadaka, R. verfasserin aut Sadok, H. verfasserin aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 77(2017), 4 vom: 31. Mai, Seite 1069-1092 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:77 year:2017 number:4 day:31 month:05 pages:1069-1092 https://dx.doi.org/10.1007/s11075-017-0353-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 77 2017 4 31 05 1069-1092
allfieldsSound	10.1007/s11075-017-0353-6 doi (DE-627)SPR016430484 (SPR)s11075-017-0353-6-e DE-627 ger DE-627 rakwb eng 510 ASE 31.76 bkl Messaoudi, A. verfasserin aut New algorithm for computing the Hermite interpolation polynomial 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let x0, x1,⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xi ≠ xj, for i ≠ j) and yi, k, for i = 0,1,⋯ , n, and k = 0 ,1 ,⋯ , ni, with ni ≥ 1, be given of real numbers, we know that there exists a unique polynomial pN − 1(x) of degree N − 1 where $N={\sum }_{i=0}^{n}(n_{i}+1)$, such that $p_{N-1}^{(k)}(x_{i})=y_{i,k}$, for i = 0,1,⋯ , n and k = 0,1,⋯ , ni. PN−1(x) is the Hermite interpolation polynomial for the set {(xi, yi, k), i = 0,1,⋯ , n, k = 0,1,⋯ , ni}. The polynomial pN−1(x) can be computed by using the Lagrange polynomials. This paper presents a new method for computing Hermite interpolation polynomials, for a particular case ni = 1. We will reformulate the Hermite interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Matrix Recursive Polynomial Interpolation Algorithm (MRPIA). Some properties of this algorithm will be studied and some examples will also be given. Polynomial interpolation (dpeaa)DE-He213 Hermite interpolation polynomials (dpeaa)DE-He213 Schur complement (dpeaa)DE-He213 Matrix Sylvester identity (dpeaa)DE-He213 Recursive polynomial interpolation algorithm (dpeaa)DE-He213 Matrix recursive interpolation algorithm (dpeaa)DE-He213 Sadaka, R. verfasserin aut Sadok, H. verfasserin aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 77(2017), 4 vom: 31. Mai, Seite 1069-1092 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:77 year:2017 number:4 day:31 month:05 pages:1069-1092 https://dx.doi.org/10.1007/s11075-017-0353-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.76 ASE AR 77 2017 4 31 05 1069-1092
language	English
source	Enthalten in Numerical algorithms 77(2017), 4 vom: 31. Mai, Seite 1069-1092 volume:77 year:2017 number:4 day:31 month:05 pages:1069-1092
sourceStr	Enthalten in Numerical algorithms 77(2017), 4 vom: 31. Mai, Seite 1069-1092 volume:77 year:2017 number:4 day:31 month:05 pages:1069-1092
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Polynomial interpolation Hermite interpolation polynomials Schur complement Matrix Sylvester identity Recursive polynomial interpolation algorithm Matrix recursive interpolation algorithm
dewey-raw	510
isfreeaccess_bool	false
container_title	Numerical algorithms
authorswithroles_txt_mv	Messaoudi, A. @@aut@@ Sadaka, R. @@aut@@ Sadok, H. @@aut@@
publishDateDaySort_date	2017-05-31T00:00:00Z
hierarchy_top_id	318468581
dewey-sort	3510
id	SPR016430484
language_de	englisch
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author	Messaoudi, A.
spellingShingle	Messaoudi, A. ddc 510 bkl 31.76 misc Polynomial interpolation misc Hermite interpolation polynomials misc Schur complement misc Matrix Sylvester identity misc Recursive polynomial interpolation algorithm misc Matrix recursive interpolation algorithm New algorithm for computing the Hermite interpolation polynomial
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topic_title	510 ASE 31.76 bkl New algorithm for computing the Hermite interpolation polynomial Polynomial interpolation (dpeaa)DE-He213 Hermite interpolation polynomials (dpeaa)DE-He213 Schur complement (dpeaa)DE-He213 Matrix Sylvester identity (dpeaa)DE-He213 Recursive polynomial interpolation algorithm (dpeaa)DE-He213 Matrix recursive interpolation algorithm (dpeaa)DE-He213
topic	ddc 510 bkl 31.76 misc Polynomial interpolation misc Hermite interpolation polynomials misc Schur complement misc Matrix Sylvester identity misc Recursive polynomial interpolation algorithm misc Matrix recursive interpolation algorithm
topic_unstemmed	ddc 510 bkl 31.76 misc Polynomial interpolation misc Hermite interpolation polynomials misc Schur complement misc Matrix Sylvester identity misc Recursive polynomial interpolation algorithm misc Matrix recursive interpolation algorithm
topic_browse	ddc 510 bkl 31.76 misc Polynomial interpolation misc Hermite interpolation polynomials misc Schur complement misc Matrix Sylvester identity misc Recursive polynomial interpolation algorithm misc Matrix recursive interpolation algorithm
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title	New algorithm for computing the Hermite interpolation polynomial
ctrlnum	(DE-627)SPR016430484 (SPR)s11075-017-0353-6-e
title_full	New algorithm for computing the Hermite interpolation polynomial
author_sort	Messaoudi, A.
journal	Numerical algorithms
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author_browse	Messaoudi, A. Sadaka, R. Sadok, H.
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title_sort	new algorithm for computing the hermite interpolation polynomial
title_auth	New algorithm for computing the Hermite interpolation polynomial
abstract	Abstract Let x0, x1,⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xi ≠ xj, for i ≠ j) and yi, k, for i = 0,1,⋯ , n, and k = 0 ,1 ,⋯ , ni, with ni ≥ 1, be given of real numbers, we know that there exists a unique polynomial pN − 1(x) of degree N − 1 where $N={\sum }_{i=0}^{n}(n_{i}+1)$, such that $p_{N-1}^{(k)}(x_{i})=y_{i,k}$, for i = 0,1,⋯ , n and k = 0,1,⋯ , ni. PN−1(x) is the Hermite interpolation polynomial for the set {(xi, yi, k), i = 0,1,⋯ , n, k = 0,1,⋯ , ni}. The polynomial pN−1(x) can be computed by using the Lagrange polynomials. This paper presents a new method for computing Hermite interpolation polynomials, for a particular case ni = 1. We will reformulate the Hermite interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Matrix Recursive Polynomial Interpolation Algorithm (MRPIA). Some properties of this algorithm will be studied and some examples will also be given.
abstractGer	Abstract Let x0, x1,⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xi ≠ xj, for i ≠ j) and yi, k, for i = 0,1,⋯ , n, and k = 0 ,1 ,⋯ , ni, with ni ≥ 1, be given of real numbers, we know that there exists a unique polynomial pN − 1(x) of degree N − 1 where $N={\sum }_{i=0}^{n}(n_{i}+1)$, such that $p_{N-1}^{(k)}(x_{i})=y_{i,k}$, for i = 0,1,⋯ , n and k = 0,1,⋯ , ni. PN−1(x) is the Hermite interpolation polynomial for the set {(xi, yi, k), i = 0,1,⋯ , n, k = 0,1,⋯ , ni}. The polynomial pN−1(x) can be computed by using the Lagrange polynomials. This paper presents a new method for computing Hermite interpolation polynomials, for a particular case ni = 1. We will reformulate the Hermite interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Matrix Recursive Polynomial Interpolation Algorithm (MRPIA). Some properties of this algorithm will be studied and some examples will also be given.
abstract_unstemmed	Abstract Let x0, x1,⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xi ≠ xj, for i ≠ j) and yi, k, for i = 0,1,⋯ , n, and k = 0 ,1 ,⋯ , ni, with ni ≥ 1, be given of real numbers, we know that there exists a unique polynomial pN − 1(x) of degree N − 1 where $N={\sum }_{i=0}^{n}(n_{i}+1)$, such that $p_{N-1}^{(k)}(x_{i})=y_{i,k}$, for i = 0,1,⋯ , n and k = 0,1,⋯ , ni. PN−1(x) is the Hermite interpolation polynomial for the set {(xi, yi, k), i = 0,1,⋯ , n, k = 0,1,⋯ , ni}. The polynomial pN−1(x) can be computed by using the Lagrange polynomials. This paper presents a new method for computing Hermite interpolation polynomials, for a particular case ni = 1. We will reformulate the Hermite interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Matrix Recursive Polynomial Interpolation Algorithm (MRPIA). Some properties of this algorithm will be studied and some examples will also be given.
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title_short	New algorithm for computing the Hermite interpolation polynomial
url	https://dx.doi.org/10.1007/s11075-017-0353-6
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author2	Sadaka, R. Sadok, H.
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doi_str	10.1007/s11075-017-0353-6
up_date	2024-07-03T23:01:34.990Z
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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">SPR016430484</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220111031837.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201006s2017 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11075-017-0353-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR016430484</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s11075-017-0353-6-e</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">510</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.76</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Messaoudi, A.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">New algorithm for computing the Hermite interpolation polynomial</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let x0, x1,⋯ , xn, be a set of n + 1 distinct real numbers (i.e., xi ≠ xj, for i ≠ j) and yi, k, for i = 0,1,⋯ , n, and k = 0 ,1 ,⋯ , ni, with ni ≥ 1, be given of real numbers, we know that there exists a unique polynomial pN − 1(x) of degree N − 1 where $N={\sum }_{i=0}^{n}(n_{i}+1)$, such that $p_{N-1}^{(k)}(x_{i})=y_{i,k}$, for i = 0,1,⋯ , n and k = 0,1,⋯ , ni. PN−1(x) is the Hermite interpolation polynomial for the set {(xi, yi, k), i = 0,1,⋯ , n, k = 0,1,⋯ , ni}. The polynomial pN−1(x) can be computed by using the Lagrange polynomials. This paper presents a new method for computing Hermite interpolation polynomials, for a particular case ni = 1. We will reformulate the Hermite interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Matrix Recursive Polynomial Interpolation Algorithm (MRPIA). Some properties of this algorithm will be studied and some examples will also be given.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polynomial interpolation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hermite interpolation polynomials</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Schur complement</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrix Sylvester identity</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Recursive polynomial interpolation algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrix recursive interpolation algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sadaka, R.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sadok, H.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Numerical algorithms</subfield><subfield code="d">Bussum : Baltzer, 1991</subfield><subfield code="g">77(2017), 4 vom: 31. Mai, Seite 1069-1092</subfield><subfield code="w">(DE-627)318468581</subfield><subfield code="w">(DE-600)2002650-X</subfield><subfield code="x">1572-9265</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:77</subfield><subfield code="g">year:2017</subfield><subfield code="g">number:4</subfield><subfield code="g">day:31</subfield><subfield code="g">month:05</subfield><subfield code="g">pages:1069-1092</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s11075-017-0353-6</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield 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