Pseudocomposition: A technique to design predictor–corrector methods for systems of nonlinear equations

Cordero, Alicia; Torregrosa, Juan R.; Vassileva, María P.

doi:10.1016/j.amc.2012.04.081

Cited by 31 publications

(25 citation statements)

References 17 publications

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“…By applying the next result, it is known (see [5]) that, the pseudocomposition technique allows us to design methods with higher order of convergence.…”

Section: Proposed High-order Methodsmentioning

confidence: 99%

See 1 more Smart Citation

New Family of Iterative Methods with High Order of Convergence for Solving Nonlinear Systems

Cordero

Torregrosa

Vassileva

2013

Lecture Notes in Computer Science

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Abstract.In this paper we present and analyze a set of predictor-corrector iterative methods with increasing order of convergence, for solving systems of nonlinear equations. Our aim is to achieve high order of convergence with few Jacobian and/or functional evaluations. On the other hand, by applying the pseudocomposition technique on each proposed scheme we get to increase their order of convergence, obtaining new high-order and efficient methods. We use the classical efficiency index in order to compare the obtained schemes and make some numerical test.

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“…By applying the next result, it is known (see [5]) that, the pseudocomposition technique allows us to design methods with higher order of convergence.…”

Section: Proposed High-order Methodsmentioning

confidence: 99%

“…The pseudocomposition technique (see [5]) consists of the following: we consider a method of order of convergence p as a predictor, whose penultimate step is of order q, and then we use a corrector step based on the Gaussian quadrature. So, we obtain a family of iterative schemes whose order of convergence is min{q+p, 3q}.…”

Section: Introductionmentioning

confidence: 99%

New Family of Iterative Methods with High Order of Convergence for Solving Nonlinear Systems

Cordero

Torregrosa

Vassileva

2013

Lecture Notes in Computer Science

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“…Among others, several modifications of Newton's method and its variants were proposed to reduce computational cost, accelerate the convergence and reduce evaluations of functions in each step of the 131 iterations (see [3][4][5]7,17,22] and references therein). Just like quadrature rules have been used to propose Newtonlike methods [17,[19][20][21][22], some efforts at using quadrature formulas to propose Broyden-like methods includes those of [13,14], all of which are directed towards the development of cost effective approaches.…”

Section: Introductionmentioning

confidence: 99%

Quadrature based Broyden-like method for systems of nonlinear equations

Osinuga

Yusuff

2018

Stat., optim. inf. comput.

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A new iterative method based on the quasi-Newton approach for solving systems of nonlinear equations, especially large scale is proposed. We used the weighted combination of the Trapezoidal and Simpson quadrature rules. Our goal is to enhance the efficiency of the well known Broyden method by reducing the number of iterations it takes to reach a solution. Local convergence analysis and computational results are given.

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“…The pseudocomposition technique (see [10]) consists of the following: we consider a method of order of convergence p as a predictor, whose penultimate step is of order q, and then we use a corrector step based on the Gaussian quadrature. So, we obtain a family of iterative schemes whose order of convergence is min{q + p, 3q}.…”

Section: Introductionmentioning

confidence: 99%

“…It is known (see [10]) that, by applying the pseudocomposition technique, it is possible to design methods with higher order of convergence. We will see in the following how this technique modify the properties of the proposed schemes.…”

mentioning

confidence: 99%

Increasing the order of convergence of iterative schemes for solving nonlinear systems

Cordero

Torregrosa

Vassileva

2013

Journal of Computational and Applied Mathematics

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A set of multistep iterative methods with increasing order of convergence is presented, for solving systems of nonlinear equations. One of the main advantages of these schemes is to achieve high order of convergence with few Jacobian and functional evaluations, joint with the use of the same matrix of coefficients in the most of the linear systems involved in the process. Indeed, the application of the pseudocomposition technique on these proposed schemes allows us to increase their order of convergence, obtaining new high-order, efficient methods. Finally, some numerical tests are performed in order to check their practical behavior.

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Pseudocomposition: A technique to design predictor–corrector methods for systems of nonlinear equations

Cited by 31 publications

References 17 publications

New Family of Iterative Methods with High Order of Convergence for Solving Nonlinear Systems

New Family of Iterative Methods with High Order of Convergence for Solving Nonlinear Systems

Quadrature based Broyden-like method for systems of nonlinear equations

Increasing the order of convergence of iterative schemes for solving nonlinear systems

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