Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems

DOI10.1137/S0895479899359837zbMath0982.65040OpenAlexW2144917506MaRDI QIDQ2706305

Françoise Tisseur

Publication date: 19 March 2001

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0895479899359837

zbMATH Keywords

Newton's methodnumerical examplesbackward stabilityrounding error analysisiterative refinementCholesky methodsymmetric generalized eigenvalue problemextended precisionfloating point arithmetics

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (18)

Mixed precision algorithms in numerical linear algebra ⋮ Iterative refinement for symmetric eigenvalue decomposition ⋮ Iterative refinement for ill-conditioned linear systems ⋮ On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots ⋮ Mixed-precision explicit stabilized Runge-Kutta methods for single- and multi-scale differential equations ⋮ Parallel iterative refinement in polynomial eigenvalue problems ⋮ An eigenvalue search method using the Orr-Sommerfeld equation for shear flow ⋮ How accurate does Newton have to be? ⋮ Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions ⋮ Unnamed Item ⋮ Continuous methods for symmetric generalized eigenvalue problems ⋮ Mixed precision path tracking for polynomial homotopy continuation ⋮ Accurate polynomial root-finding methods for symmetric tridiagonal matrix eigenproblems ⋮ Perturbation, extraction and refinement of invariant pairs for matrix polynomials ⋮ Accurate simple zeros of polynomials in floating point arithmetic ⋮ Subdivision-Based Nonlinear Multiscale Cloth Simulation ⋮ An Algorithm for Quadratic Eigenproblems with Low Rank Damping ⋮ Perturbation theory for homogeneous polynomial eigenvalue problems

Uses Software

• mctoolbox

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