A new second order Taylor-like theorem with an optimized reduced remainder

In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [ a , b...
Ausführliche Beschreibung

In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [ a , b ] , this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [ a , b ] , together with f ′ ′ ( a ) and f ′ ′ ( b ) . We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P 2 - interpolation error estimate and the error bound of the Simpson rule in numerical integration. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Chaskalovic, Joël [verfasserIn] Assous, Franck [verfasserIn] Jamshidipour, Hessam [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Taylor’s theorem Lagrange interpolation Interpolation error Simpson rule Quadrature error

Übergeordnetes Werk:	Enthalten in: Journal of computational and applied mathematics - Amsterdam [u.a.] : North-Holland, 1975, 438
Übergeordnetes Werk:	volume:438

DOI / URN:	10.1016/j.cam.2023.115496

Katalog-ID:	ELV065207165

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245	1	0	\|a A new second order Taylor-like theorem with an optimized reduced remainder
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520			\|a In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [ a , b ] , this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [ a , b ] , together with f ′ ′ ( a ) and f ′ ′ ( b ) . We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P 2 - interpolation error estimate and the error bound of the Simpson rule in numerical integration.
650		4	\|a Taylor’s theorem
650		4	\|a Lagrange interpolation
650		4	\|a Interpolation error
650		4	\|a Simpson rule
650		4	\|a Quadrature error
700	1		\|a Assous, Franck \|e verfasserin \|4 aut
700	1		\|a Jamshidipour, Hessam \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Journal of computational and applied mathematics \|d Amsterdam [u.a.] : North-Holland, 1975 \|g 438 \|h Online-Ressource \|w (DE-627)266889204 \|w (DE-600)1468806-2 \|w (DE-576)075962373 \|7 nnns
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912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
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912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2122
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912			\|a GBV_ILN_2143
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matchkey_str	chaskalovicjolassousfranckjamshidipourhe:2023----:nweodretyolktermihnpii
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allfields	10.1016/j.cam.2023.115496 doi (DE-627)ELV065207165 (ELSEVIER)S0377-0427(23)00440-5 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Chaskalovic, Joël verfasserin aut A new second order Taylor-like theorem with an optimized reduced remainder 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [ a , b ] , this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [ a , b ] , together with f ′ ′ ( a ) and f ′ ′ ( b ) . We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P 2 - interpolation error estimate and the error bound of the Simpson rule in numerical integration. Taylor’s theorem Lagrange interpolation Interpolation error Simpson rule Quadrature error Assous, Franck verfasserin aut Jamshidipour, Hessam verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 438 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:438 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 438
spelling	10.1016/j.cam.2023.115496 doi (DE-627)ELV065207165 (ELSEVIER)S0377-0427(23)00440-5 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Chaskalovic, Joël verfasserin aut A new second order Taylor-like theorem with an optimized reduced remainder 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [ a , b ] , this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [ a , b ] , together with f ′ ′ ( a ) and f ′ ′ ( b ) . We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P 2 - interpolation error estimate and the error bound of the Simpson rule in numerical integration. Taylor’s theorem Lagrange interpolation Interpolation error Simpson rule Quadrature error Assous, Franck verfasserin aut Jamshidipour, Hessam verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 438 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:438 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 438
allfields_unstemmed	10.1016/j.cam.2023.115496 doi (DE-627)ELV065207165 (ELSEVIER)S0377-0427(23)00440-5 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Chaskalovic, Joël verfasserin aut A new second order Taylor-like theorem with an optimized reduced remainder 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [ a , b ] , this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [ a , b ] , together with f ′ ′ ( a ) and f ′ ′ ( b ) . We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P 2 - interpolation error estimate and the error bound of the Simpson rule in numerical integration. Taylor’s theorem Lagrange interpolation Interpolation error Simpson rule Quadrature error Assous, Franck verfasserin aut Jamshidipour, Hessam verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 438 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:438 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 438
allfieldsGer	10.1016/j.cam.2023.115496 doi (DE-627)ELV065207165 (ELSEVIER)S0377-0427(23)00440-5 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Chaskalovic, Joël verfasserin aut A new second order Taylor-like theorem with an optimized reduced remainder 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [ a , b ] , this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [ a , b ] , together with f ′ ′ ( a ) and f ′ ′ ( b ) . We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P 2 - interpolation error estimate and the error bound of the Simpson rule in numerical integration. Taylor’s theorem Lagrange interpolation Interpolation error Simpson rule Quadrature error Assous, Franck verfasserin aut Jamshidipour, Hessam verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 438 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:438 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 438
allfieldsSound	10.1016/j.cam.2023.115496 doi (DE-627)ELV065207165 (ELSEVIER)S0377-0427(23)00440-5 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Chaskalovic, Joël verfasserin aut A new second order Taylor-like theorem with an optimized reduced remainder 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [ a , b ] , this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [ a , b ] , together with f ′ ′ ( a ) and f ′ ′ ( b ) . We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P 2 - interpolation error estimate and the error bound of the Simpson rule in numerical integration. Taylor’s theorem Lagrange interpolation Interpolation error Simpson rule Quadrature error Assous, Franck verfasserin aut Jamshidipour, Hessam verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 438 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:438 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 438
language	English
source	Enthalten in Journal of computational and applied mathematics 438 volume:438
sourceStr	Enthalten in Journal of computational and applied mathematics 438 volume:438
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topic_facet	Taylor’s theorem Lagrange interpolation Interpolation error Simpson rule Quadrature error
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authorswithroles_txt_mv	Chaskalovic, Joël @@aut@@ Assous, Franck @@aut@@ Jamshidipour, Hessam @@aut@@
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author	Chaskalovic, Joël
spellingShingle	Chaskalovic, Joël ddc 510 bkl 31.00 misc Taylor’s theorem misc Lagrange interpolation misc Interpolation error misc Simpson rule misc Quadrature error A new second order Taylor-like theorem with an optimized reduced remainder
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topic_title	510 VZ 31.00 bkl A new second order Taylor-like theorem with an optimized reduced remainder Taylor’s theorem Lagrange interpolation Interpolation error Simpson rule Quadrature error
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title	A new second order Taylor-like theorem with an optimized reduced remainder
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title_full	A new second order Taylor-like theorem with an optimized reduced remainder
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author_browse	Chaskalovic, Joël Assous, Franck Jamshidipour, Hessam
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title_sort	a new second order taylor-like theorem with an optimized reduced remainder
title_auth	A new second order Taylor-like theorem with an optimized reduced remainder
abstract	In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [ a , b ] , this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [ a , b ] , together with f ′ ′ ( a ) and f ′ ′ ( b ) . We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P 2 - interpolation error estimate and the error bound of the Simpson rule in numerical integration.
abstractGer	In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [ a , b ] , this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [ a , b ] , together with f ′ ′ ( a ) and f ′ ′ ( b ) . We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P 2 - interpolation error estimate and the error bound of the Simpson rule in numerical integration.
abstract_unstemmed	In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [ a , b ] , this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [ a , b ] , together with f ′ ′ ( a ) and f ′ ′ ( b ) . We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P 2 - interpolation error estimate and the error bound of the Simpson rule in numerical integration.
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title_short	A new second order Taylor-like theorem with an optimized reduced remainder
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For a given function f defined on the interval [ a , b ] , this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [ a , b ] , together with f ′ ′ ( a ) and f ′ ′ ( b ) . We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. 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A new second order Taylor-like theorem with an optimized reduced remainder

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