USYMLQ and USYMQR algorithms generalize SYMMLQ and MINRES for solving large, sparse, unsymmetric linear system of equations. In the symmetric case, USYMLQ falls back to SYMMLQ and USYMQR falls back to MINRES. It is based on an efficient orthogonal tridiagonalization procedure described in Saunders et al. 1988 paper "Two Conjugate-Gradient-Type Methods For Unsymmetric Linear Equations". USYMLQ can be used for square or under-determined systems, whereas USYMQR can be used for square, under-determined, and over-determined systems. They are iterative solvers and each step has O(N) operations; the overall storage is O(N) as well (unlike GMRES).
The solver was implemented in templated C++ with Eigen as backend linear algebra library. It has no external dependency otherwise.
This is part of my final project for CME338 at Stanford, taught by Michael Saunders.
To build the project, simply run
make
The solver encapsulates the tridiagonalization and linear solve. Below is an example of how to use it:
// ... define A and b and ...
T_Vector x;
T rnorm;
USYM_Linear_Solver<T,T_Vector,T_Matrix> solver(A,b);
solver.Initialize();
solver.Set_Mode(USYMQR);
solver.SetMaxIteration(2000);
solver.Set_Tol(1E-12, 1E-12);
solver.Solve(x, rnorm);
Please see src/tests for more examples.
Please see doc/documentation.pdf for more detailed analysis and
solver testing.
Author: Jui-Hsien Wang