The grand four: affine invariant globalizations of Newton's method

DOI10.1007/s10013-018-0301-3OpenAlexW2888102836WikidataQ129400321 ScholiaQ129400321MaRDI QIDQ1633768

Peter Deuflhard

Publication date: 20 December 2018

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10013-018-0301-3

zbMATH Keywords

affine invarianceglobal Newton methodsnatural level functionpseudo-continuation method

Mathematics Subject Classification ID

General theory of numerical analysis in abstract spaces (65J05) Numerical optimization and variational techniques (65K10) Numerical solutions to equations with nonlinear operators (65J15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical methods for differential-algebraic equations (65L80)

Related Items (3)

A partitioned quasi-likelihood for distributed statistical inference ⋮ A sequential homotopy method for mathematical programming problems ⋮ A flow perspective on nonlinear least-squares problems

Uses Software

• NewtonLib
• ALCON

Cites Work

• A stepsize control for continuation methods and its special application to multiple shooting techniques
• A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting
• A modified continuation method for the numerical solution of nonlinear two-point boundary value problems by shooting techniques
• Fast secant methods for the iterative solution of large nonsymmetric linear systems
• Efficient Numerical Pathfollowing Beyond Critical Points
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Convergence Analysis of Pseudo-Transient Continuation
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