Premium
A robust incomplete factorization based on value and space constraints
Author(s) -
Suarjana Made,
Law Kincho H.
Publication year - 1995
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.1620381007
Subject(s) - preconditioner , incomplete cholesky factorization , incomplete lu factorization , conjugate gradient method , factorization , conjugate residual method , matrix decomposition , mathematics , matrix (chemical analysis) , positive definite matrix , dixon's factorization method , mathematical optimization , stability (learning theory) , computation , computer science , algorithm , gradient descent , iterative method , artificial intelligence , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , composite material , machine learning , artificial neural network
This paper describes an incomplete factorization method for computing a preconditioning matrix for the conjugate gradient method. The incomplete factorization satisfies the stability requirement that the incomplete factor remains positive definite throughout the factorization. When selecting a preconditioner for the conjugate gradient method, the number of non‐zero entries to be retained in the incomplete factor should be limited so that the amount of computations involving the preconditioning matrix is minimized. This paper introduces a method to generate an effective preconditioning matrix within a predefined space. Numerical results are presented to demonstrate the effectiveness of the incomplete factor as a preconditioner for the conjugate gradient method for solving large‐scale structural engineering problems.