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A truncated Newton–Lanczos method for overcoming limit and bifurcation points
Author(s) -
Papadrakakis M.
Publication year - 1990
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620290511
Subject(s) - lanczos resampling , mathematics , tridiagonal matrix , eigenvalues and eigenvectors , iterative method , limit (mathematics) , inverse iteration , convergence (economics) , bifurcation , matrix (chemical analysis) , lanczos algorithm , factorization , mathematical analysis , mathematical optimization , algorithm , nonlinear system , physics , materials science , quantum mechanics , economics , composite material , economic growth
In this study procedures for overcoming limit and bifurcation points in large‐scale structural analysis problems are described and evaluated. The methods are based on Newton's method for the outer iterations, while for the linearized problem in each iteration the preconditioned truncated Lanczos method is employed. Special care is placed upon line search routines for accelerating the convergence properties and enhancing the stability of the outer method. The proposed methodology retains all characteristics of an iterative method by avoiding the factorization of the current stiffness matrix. The necessary eigenvalue information is retained in the tridiagonal matrix of the Lanczos approach.