Accelerated Inexact Newton Schemes for Large Systems of Nonlinear Equations

DOI10.1137/S1064827595296148zbMath0916.65050OpenAlexW2010775269MaRDI QIDQ4389264

Gerard L. G. Sleijpen, Henk A. van der Vorst, Diederik R. Fokkema

Publication date: 12 May 1998

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s1064827595296148

zbMATH Keywords

inexact Newton methodsconvergence accelerationnumerical experimentsGMRESJacobi iterationKrylov subspace methodsJacobi-Davidson methodArnoldi methodlinear eigenproblems

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of solutions to systems of equations (65H10)

Related Items

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Uses Software

• JDQZ

Cites Work

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• Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• Generalizations of Davidson's method for computing eigenvalues of large nonsymmetric matrices
• The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
• On nonlinear generalized conjugate gradient methods
• Generalized conjugate gradient squared
• Hybrid Krylov Methods for Nonlinear Systems of Equations
• Continuation-Conjugate Gradient Methods for the Least Squares Solution of Nonlinear Boundary Value Problems
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• Inexact Newton Methods
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
• A class of first order factorization methods
• The Davidson Method
• On a Class of Nonlinear Equation Solvers Based on the Residual Norm Reduction over a Sequence of Affine Subspaces
• Approximate solutions and eigenvalue bounds from Krylov subspaces
• GMRESR: a family of nested GMRES methods
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• The principle of minimized iterations in the solution of the matrix eigenvalue problem