A Derivative Free Newton-Like Method With Improved Rational Approximation Model for Solving Nonlinear Equation

Kamfa, Kamilu; Waziri, Mohammed Yusuf; Mamat, Mustafa; Mohamed, Mohamad Afendee

doi:10.17654/ms105010119

Cited by 5 publications

(3 citation statements)

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“…Other Quasi-Newton methods include the Symmetric Rank 1 (SR1) method and the Davidon-Fletcher-Powell (DFP) method among others. Quasi-Newton methods were utilized to find solutions to SNEs in articles [146,147,148,149,150,151,152,153,154].…”

Section: Quasi-newton Methods For Finding Rootsmentioning

confidence: 99%

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

Kotsireas¹,

Pardalos²,

Semenov³

et al. 2022

Preprint

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This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting a thorough description and analysis of the known methods capable of finding one or many solutions to SNEs, and to assist interested readers seeking to identify solution techniques which are well suited for solving the various classes of SNEs which one may encounter in real world applications.To accomplish these objectives, we present a multi-part survey. In part one, we focus on root-finding approaches which can be used to search for solutions to a SNE without transforming it into an optimization problem. In part two, we will introduce the various transformations which have been utilized to transform a SNE into an optimization problem, and we discuss optimization algorithms which can then be used to search for solutions. In part three, we will present a robust quantitative comparative analysis of methods capable of searching for solutions to SNEs.

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Section: Quasi-newton Methods For Finding Rootsmentioning

confidence: 99%

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

Kotsireas¹,

Pardalos²,

Semenov³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…For this reason, [15] highlighted the importance of starting the process with the steepest descent direction, i.e. d 0 = −g 0 [16], otherwise, the convergence rate will be linear even for a strongly convex quadratic function [17]. The successive directions are obtained in a predefined sequence, defined as…”

Section: Introductionmentioning

confidence: 99%

Performance evaluation of a novel Conjugate Gradient Method for training feed forward neural network

Kamilu¹,

Sulaiman²,

Muhammad³

et al. 2023

Math. Model. Comput.

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In this paper, we construct a new conjugate gradient method for solving unconstrained optimization problems. The proposed method satisfies the sufficient decent property irrespective of the line search and the global convergence was established under some suitable. Further, the new method was used to train different sets of data via a feed forward neural network. Results obtained show that the proposed algorithm significantly reduces the computational time by speeding up the directional minimization with a faster convergence rate.

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“…Differential equations play a major role in chemical kinetics, biological models, fluid dynamics, just like in nonlinear equations [17,18]. Many mathematical formulations of physical phenomena that are modeled under the differential sences usually produce an integro-differential equation (IDE), a differential equation (DE), or likely give an integral equation (IE).…”

Section: Introductionmentioning

confidence: 99%

An Efficient Algorithm for Solving Classes of Integral and Integro-differential Equations

Al-Ahma¹,

Sulaiman²,

Mamat³

2020

IJETT

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This paper develops a numerical approximation technique based on the structure of differential transform method (DTM), Laplace transform (LT) procedure and Padé approximants (PA) scheme for solving integral and integro-differential equations. The proposed method which gives a virtuous approximation for the true solution in a large region is referred to modified differential transform method (MDTM). Some numerical problems are given to illustrates the efficiency and applicability of the method. Numerical results have shown that the MDTM method is promising for solving integral and integro-differential e quations.

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A Derivative Free Newton-Like Method With Improved Rational Approximation Model for Solving Nonlinear Equation

Cited by 5 publications

References 0 publications

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

Performance evaluation of a novel Conjugate Gradient Method for training feed forward neural network

An Efficient Algorithm for Solving Classes of Integral and Integro-differential Equations

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