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Systems Optimization Laboratory

Stanford University
Dept of Management Science and Engineering (MS&E)

Huang Engineering Center

Stanford, CA 94305-4121  USA

SYMMLQ: Sparse Symmetric Equations

  • AUTHORS: C. C. Paige, M. A. Saunders.
  • CONTRIBUTORS: Jeffery Kline, Dominique Orban.
  • CONTENTS: Implementation of a conjugate-gradient type method for solving sparse linear equations:  Solve \begin{align*} Ax = b \ \text{ or } \ (A - sI)x = b. \end{align*} The matrix \(A - sI\) must be symmetric and nonsingular, but it may be definite or indefinite. The scalar \(s\) is a shifting parameter -- it may be any number. The method is based on Lanczos tridiagonalization. You may provide a preconditioner, but it must be positive definite.

    If A - sI is symmetric but singular, use MINRES.
    If A is unsymmetric, use LSQR.
    C. C. Paige and M. A. Saunders (1975). Solution of sparse indefinite systems of linear equations, SINUM 12, 617--629.