Improved bracketing parabolic method for numerical solution of nonlinear equations

An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the spe...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Kodnyanko, Vladimir [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Nonlinear equation Bisection method Müller method Brent method Ridders method Parabolic method Improved parabolic method Speed method

Übergeordnetes Werk:	Enthalten in: Applied mathematics and computation - New York, NY : Elsevier, 1975, 400
Übergeordnetes Werk:	volume:400

DOI / URN:	10.1016/j.amc.2021.125995

Katalog-ID:	ELV005653037

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520			\|a An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the specified accuracy of the solution. Based on the data obtained, an improved parabolic method that guarantees accuracy confirmed by computational experiment is developed. This proposed method combines the quadratic speed of parabolic approaches and the ability to provide stable convergence to the solution for slowly varying functions inherent to the bisection method.
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650		4	\|a Müller method
650		4	\|a Brent method
650		4	\|a Ridders method
650		4	\|a Parabolic method
650		4	\|a Improved parabolic method
650		4	\|a Speed method
773	0	8	\|i Enthalten in \|t Applied mathematics and computation \|d New York, NY : Elsevier, 1975 \|g 400 \|h Online-Ressource \|w (DE-627)26555022X \|w (DE-600)1465428-3 \|w (DE-576)078314976 \|7 nnns
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allfields	10.1016/j.amc.2021.125995 doi (DE-627)ELV005653037 (ELSEVIER)S0096-3003(21)00043-6 DE-627 ger DE-627 rda eng 510 DE-600 31.80 bkl 31.76 bkl Kodnyanko, Vladimir verfasserin aut Improved bracketing parabolic method for numerical solution of nonlinear equations 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the specified accuracy of the solution. Based on the data obtained, an improved parabolic method that guarantees accuracy confirmed by computational experiment is developed. This proposed method combines the quadratic speed of parabolic approaches and the ability to provide stable convergence to the solution for slowly varying functions inherent to the bisection method. Nonlinear equation Bisection method Müller method Brent method Ridders method Parabolic method Improved parabolic method Speed method Enthalten in Applied mathematics and computation New York, NY : Elsevier, 1975 400 Online-Ressource (DE-627)26555022X (DE-600)1465428-3 (DE-576)078314976 nnns volume:400 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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_63 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_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.80 Angewandte Mathematik 31.76 Numerische Mathematik AR 400
spelling	10.1016/j.amc.2021.125995 doi (DE-627)ELV005653037 (ELSEVIER)S0096-3003(21)00043-6 DE-627 ger DE-627 rda eng 510 DE-600 31.80 bkl 31.76 bkl Kodnyanko, Vladimir verfasserin aut Improved bracketing parabolic method for numerical solution of nonlinear equations 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the specified accuracy of the solution. Based on the data obtained, an improved parabolic method that guarantees accuracy confirmed by computational experiment is developed. This proposed method combines the quadratic speed of parabolic approaches and the ability to provide stable convergence to the solution for slowly varying functions inherent to the bisection method. Nonlinear equation Bisection method Müller method Brent method Ridders method Parabolic method Improved parabolic method Speed method Enthalten in Applied mathematics and computation New York, NY : Elsevier, 1975 400 Online-Ressource (DE-627)26555022X (DE-600)1465428-3 (DE-576)078314976 nnns volume:400 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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_63 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_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.80 Angewandte Mathematik 31.76 Numerische Mathematik AR 400
allfields_unstemmed	10.1016/j.amc.2021.125995 doi (DE-627)ELV005653037 (ELSEVIER)S0096-3003(21)00043-6 DE-627 ger DE-627 rda eng 510 DE-600 31.80 bkl 31.76 bkl Kodnyanko, Vladimir verfasserin aut Improved bracketing parabolic method for numerical solution of nonlinear equations 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the specified accuracy of the solution. Based on the data obtained, an improved parabolic method that guarantees accuracy confirmed by computational experiment is developed. This proposed method combines the quadratic speed of parabolic approaches and the ability to provide stable convergence to the solution for slowly varying functions inherent to the bisection method. Nonlinear equation Bisection method Müller method Brent method Ridders method Parabolic method Improved parabolic method Speed method Enthalten in Applied mathematics and computation New York, NY : Elsevier, 1975 400 Online-Ressource (DE-627)26555022X (DE-600)1465428-3 (DE-576)078314976 nnns volume:400 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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_63 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_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.80 Angewandte Mathematik 31.76 Numerische Mathematik AR 400
allfieldsGer	10.1016/j.amc.2021.125995 doi (DE-627)ELV005653037 (ELSEVIER)S0096-3003(21)00043-6 DE-627 ger DE-627 rda eng 510 DE-600 31.80 bkl 31.76 bkl Kodnyanko, Vladimir verfasserin aut Improved bracketing parabolic method for numerical solution of nonlinear equations 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the specified accuracy of the solution. Based on the data obtained, an improved parabolic method that guarantees accuracy confirmed by computational experiment is developed. This proposed method combines the quadratic speed of parabolic approaches and the ability to provide stable convergence to the solution for slowly varying functions inherent to the bisection method. Nonlinear equation Bisection method Müller method Brent method Ridders method Parabolic method Improved parabolic method Speed method Enthalten in Applied mathematics and computation New York, NY : Elsevier, 1975 400 Online-Ressource (DE-627)26555022X (DE-600)1465428-3 (DE-576)078314976 nnns volume:400 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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_63 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_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.80 Angewandte Mathematik 31.76 Numerische Mathematik AR 400
allfieldsSound	10.1016/j.amc.2021.125995 doi (DE-627)ELV005653037 (ELSEVIER)S0096-3003(21)00043-6 DE-627 ger DE-627 rda eng 510 DE-600 31.80 bkl 31.76 bkl Kodnyanko, Vladimir verfasserin aut Improved bracketing parabolic method for numerical solution of nonlinear equations 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the specified accuracy of the solution. Based on the data obtained, an improved parabolic method that guarantees accuracy confirmed by computational experiment is developed. This proposed method combines the quadratic speed of parabolic approaches and the ability to provide stable convergence to the solution for slowly varying functions inherent to the bisection method. Nonlinear equation Bisection method Müller method Brent method Ridders method Parabolic method Improved parabolic method Speed method Enthalten in Applied mathematics and computation New York, NY : Elsevier, 1975 400 Online-Ressource (DE-627)26555022X (DE-600)1465428-3 (DE-576)078314976 nnns volume:400 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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_63 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_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.80 Angewandte Mathematik 31.76 Numerische Mathematik AR 400
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source	Enthalten in Applied mathematics and computation 400 volume:400
sourceStr	Enthalten in Applied mathematics and computation 400 volume:400
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topic_facet	Nonlinear equation Bisection method Müller method Brent method Ridders method Parabolic method Improved parabolic method Speed method
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author	Kodnyanko, Vladimir
spellingShingle	Kodnyanko, Vladimir ddc 510 bkl 31.80 bkl 31.76 misc Nonlinear equation misc Bisection method misc Müller method misc Brent method misc Ridders method misc Parabolic method misc Improved parabolic method misc Speed method Improved bracketing parabolic method for numerical solution of nonlinear equations
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topic_title	510 DE-600 31.80 bkl 31.76 bkl Improved bracketing parabolic method for numerical solution of nonlinear equations Nonlinear equation Bisection method Müller method Brent method Ridders method Parabolic method Improved parabolic method Speed method
topic	ddc 510 bkl 31.80 bkl 31.76 misc Nonlinear equation misc Bisection method misc Müller method misc Brent method misc Ridders method misc Parabolic method misc Improved parabolic method misc Speed method
topic_unstemmed	ddc 510 bkl 31.80 bkl 31.76 misc Nonlinear equation misc Bisection method misc Müller method misc Brent method misc Ridders method misc Parabolic method misc Improved parabolic method misc Speed method
topic_browse	ddc 510 bkl 31.80 bkl 31.76 misc Nonlinear equation misc Bisection method misc Müller method misc Brent method misc Ridders method misc Parabolic method misc Improved parabolic method misc Speed method
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title	Improved bracketing parabolic method for numerical solution of nonlinear equations
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title_full	Improved bracketing parabolic method for numerical solution of nonlinear equations
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title_sort	improved bracketing parabolic method for numerical solution of nonlinear equations
title_auth	Improved bracketing parabolic method for numerical solution of nonlinear equations
abstract	An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the specified accuracy of the solution. Based on the data obtained, an improved parabolic method that guarantees accuracy confirmed by computational experiment is developed. This proposed method combines the quadratic speed of parabolic approaches and the ability to provide stable convergence to the solution for slowly varying functions inherent to the bisection method.
abstractGer	An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the specified accuracy of the solution. Based on the data obtained, an improved parabolic method that guarantees accuracy confirmed by computational experiment is developed. This proposed method combines the quadratic speed of parabolic approaches and the ability to provide stable convergence to the solution for slowly varying functions inherent to the bisection method.
abstract_unstemmed	An analysis of numerical methods for solving algebraic and transcendental equations in terms of speed is performed. In contrast to the reliable bisection method, the well-known parabolic methods by Müller, Brent, and Ridders have been determined to have higher speed, but do not always ensure the specified accuracy of the solution. Based on the data obtained, an improved parabolic method that guarantees accuracy confirmed by computational experiment is developed. This proposed method combines the quadratic speed of parabolic approaches and the ability to provide stable convergence to the solution for slowly varying functions inherent to the bisection method.
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title_short	Improved bracketing parabolic method for numerical solution of nonlinear equations
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up_date	2024-07-06T18:42:06.071Z
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Improved bracketing parabolic method for numerical solution of nonlinear equations

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