Solution of Sparse Indefinite Systems of Linear Equations

Authors

Christopher C. Paige, Michael A. Saunders

Year

1975

Journal Paper

Algorithm

SYMMLQ

Source

SIAM Journal on Numerical Analysis

Identifiers

DOI 10.1137/0712047

Abstract¶

The method of conjugate gradients for solving systems of linear equations with a symmetric positive definite matrix A is given as a logical development of the Lanczos algorithm for tridiagonalizing A. This approach suggests numerical algorithms for solving such systems when A is symmetric but indefinite. These methods have advantages when A is large and sparse.

Summary¶

Paige and Saunders extend Lanczos and conjugate-gradient ideas to large sparse symmetric indefinite linear systems. The paper is the source of methods such as SYMMLQ and closely related MINRES-style reasoning, showing how tridiagonal Lanczos reductions can produce practical solvers beyond positive-definite systems.