Least-Change Secant Updates of Nonsquare Matrices

Least-Change Secant Updates of Nonsquare Matrices

The notion of least-change secant updates is extended to apply to nonsquare matrices in a way appropriate for quasi-Newton methods used to solve systems of nonlinear equations that depend on parameters. Extensions of the widely used least-change secant updates for square matrices are given. A local...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on numerical analysis Vol. 27; no. 5; pp. 1263 - 1294
Main Authors: Bourji, Samih K., Walker, Homer F.
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01-10-1990
Subjects:
Algorithms
Applied mathematics
Approximation
Economic theory
Exact sciences and technology
Iterative methods
Jacobians
Logical givens
Mathematics
Matrices
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Perceptron convergence procedure
Sciences and techniques of general use
Secant function
Values
Non linear equation
Algebraic equation
Newton method
Square matrix
Convergence
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The notion of least-change secant updates is extended to apply to nonsquare matrices in a way appropriate for quasi-Newton methods used to solve systems of nonlinear equations that depend on parameters. Extensions of the widely used least-change secant updates for square matrices are given. A local convergence analysis for certain paradigm iterations is outlined as motivation for the use of these updates, and numerical experiments involving these iterations are discussed.
ISSN:0036-1429
1095-7170
DOI:10.1137/0727072