Systems Optimization Laboratory
Stanford, CA 94305-4121 USA
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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.
- REFERENCES:
C. C. Paige and M. A. Saunders (1975).
Solution of sparse indefinite systems of linear equations,
SINUM 12, 617--629.
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