Local convergence analysis of tensor methods for nonlinear equations
type: Item
instance of: scholarly article
title: Local convergence analysis of tensor methods for nonlinear equations
zbMATH Open document ID: 0796.65069
DOI: 10.1007/BF01585177
author: Dan Feng
author: Paul D. Frank
author: Robert B. Schnabel
published in: Mathematical Programming. Series A. Series B
publication date: 1994-10-13T00:00:00Z
review text: The authors analyze the local convergence of two versions of tensor methods, on problems where the Jacobian at the root has a null space of rank one. It is shown that under mild conditions the sequence of iterates converges locally and two or three-step \(Q\)-superlinearly to the solution with \(Q\)-order 3/2, while standard methods converge linearly with constant converging to 1/2. The paper also confirms that tensor methods converge at least quadratically on problems where the Jacobian at the root is nonsingular.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 558704
zbMATH Keywords: superlinear convergence
zbMATH Keywords: local convergence
zbMATH Keywords: tensor methods
reviewed by: Zeke Wang
describes a project that uses: TENSOLVE
describes a project that uses: LINPACK
MaRDI profile type: Publication
cites work: Algorithm 768: TENSOLVE
cites work: Convergence Rates for Newton’s Method at Singular Points
cites work: Newton’s Method at Singular Points. I
cites work: Newton’s Method at Singular Points. II
cites work: Convergence Acceleration for Newton’s Method at Singular Points
cites work: Starlike domains of convergence for Newton's method at singularities
cites work: On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions
cites work: Analysis of Newton’s Method at Irregular Singularities
cites work: A New Acceleration Method for Newton’s Method at Singular Points
cites work: Q5661059
cites work: On Newton’s Method for Singular Problems
cites work: Tensor Methods for Unconstrained Optimization Using Second Derivatives
cites work: Tensor Methods for Nonlinear Equations
cites work: Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
description: scientific article; zbMATH DE number 558704