On the accurate determination of nonisolated solutions of nonlinear equations

DOI10.1007/BF02237950zbMath0451.65036MaRDI QIDQ1148100

Wilhelm Werner, Helmut Weber

Publication date: 1981

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

Newton's methodnonisolated solutionssingular Jacobian

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Numerical computation of solutions to systems of equations (65H10)

Related Items (13)

A relation between Newton and Gauss-Newton steps for singular nonlinear equations ⋮ A special extended system and a Newton-like method for simple singular nonlinear equations ⋮ Enlargement procedure for resolution of singularities at singular solution of nonlinear equations ⋮ An efficiently implementable Gauss-Newton-like method for solving singular nonlinear equations ⋮ A higher order method for determining nonisolated solutions of a system of nonlinear equations ⋮ A dimension-reducing method for solving systems of nonlinear equations in ⋮ Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin's \(\sin (\theta)\) theorem ⋮ Solving systems of nonlinear equations In using a rotating hyperplane in ⋮ A modified Brown algorithm for solving singular nonlinear systems with rank defects ⋮ Splitting iteration method for simple singular points and simple bifurcation points ⋮ Regularization and computation of a bifurcation problem with corank 2 ⋮ A quadratically convergent method for computing simple singular roots and its application to determining simple bifurcation points ⋮ On solving nonlinear least-squares problems in case of rankdeficient Jacobians

Cites Work

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• Über ein Verfahren der Ordnung \(1+\sqrt 2\) zur Nullstellenbestimmung
• Newton's method and high order singularities
• Some supplementary results on the \(1+\sqrt 2\) order method for the solution of nonlinear equations
• Some limit theorems for ordinary differential systems
• Convergence of the Newton process to multiple solutions
• Newton’s Method at Singular Points. I
• On Newton’s Method for Singular Problems
• Accurate Difference Methods for Nonlinear Two-Point Boundary Value Problems
• The convergence of shooting methods

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