Local convergence for some high convergence order Newton-like methods with frozen derivatives

Argyros, Ioannis K.; George, Santhosh

doi:10.1007/s40324-015-0039-8

Cited by 11 publications

(10 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Section 2, we study the semilocal convergence for the family (1). We also present the corresponding theorem for the family (2). An optimal computational study and some numerical examples are presented in Section 3.…”

Section: Theorem 1 Let X Y Be Two Banach Spaces Let B Be a Convex mentioning

confidence: 99%

See 1 more Smart Citation

On two high‐order families of frozen Newton‐type methods

Amat

Argyros

Busquier

et al. 2017

Numerical Linear Algebra App

View full text Add to dashboard Cite

SummaryThis paper is devoted to the study of two high-order families of frozen Newton-type methods. The methods are free of bilinear operators, which constitute the main limitation of the classical high-order iterative schemes.Both families are natural generalizations of an efficient third-order method.Although the methods are more demanding, a semilocal convergence analysis is presented using weaker conditions.

show abstract

Section: Theorem 1 Let X Y Be Two Banach Spaces Let B Be a Convex mentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9] The Newton method is second-order convergent under some regularity assumptions. The classical third-order methods use second-order Fréchet derivatives.…”

Section: Introductionmentioning

confidence: 99%

On two high‐order families of frozen Newton‐type methods

Amat

Argyros

Busquier

et al. 2017

Numerical Linear Algebra App

View full text Add to dashboard Cite

show abstract

“…Adopting the first sub step of the scheme in Equations (2), (5), (7) (for l = 1), (11), (13), (14) and (21), we yield…”

Section: Convergence Analysismentioning

confidence: 99%

High Convergence Order Iterative Procedures for Solving Equations Originating from Real Life Problems

Behl

Argyros

2019

Mathematics

View full text Add to dashboard Cite

The foremost aim of this paper is to suggest a local study for high order iterative procedures for solving nonlinear problems involving Banach space valued operators. We only deploy suppositions on the first-order derivative of the operator. Our conditions involve the Lipschitz or Hölder case as compared to the earlier ones. Moreover, when we specialize to these cases, they provide us: larger radius of convergence, higher bounds on the distances, more precise information on the solution and smaller Lipschitz or Hölder constants. Hence, we extend the suitability of them.Our new technique can also be used to broaden the usage of existing iterative procedures too. Finally, we check our results on a good number of numerical examples, which demonstrate that they are capable of solving such problems where earlier studies cannot apply.

show abstract

“…using Mathematical Modelling [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. The solution x * of equation (1.1) can rarely be found in an explicit form.…”

Section: Introductionmentioning

confidence: 99%

Extending the applicability of modified Newton-HSS method for solving systems of nonlinear equations

Sharma

Argyros²,

Kumar³

2018

Stud. Univ. Babes-Bolyai Math.

Self Cite

View full text Add to dashboard Cite

Abstract. We present the semilocal convergence of a modified Newton-HSS method to approximate a solution of a nonlinear equation. Earlier studies show convergence under only Lipschitz conditions limiting the applicability of this method. The convergence in this study is shown under generalized Lipschitztype conditions and restricted convergence domains. Hence, the applicability of the method is expanded. Moreover, numerical examples are also provided to show that our results can be applied to solve equations in cases where earlier study cannot be applied. Furthermore, in the cases where both old and new results are applicable, the latter provides a larger domain of convergence and tighter error bounds on the distances involved.Mathematics Subject Classification (2010): 65F10, 65W05.

show abstract

Local convergence for some high convergence order Newton-like methods with frozen derivatives

Cited by 11 publications

References 18 publications

On two high‐order families of frozen Newton‐type methods

On two high‐order families of frozen Newton‐type methods

High Convergence Order Iterative Procedures for Solving Equations Originating from Real Life Problems

Extending the applicability of modified Newton-HSS method for solving systems of nonlinear equations

Contact Info

Product

Resources

About