Extending the eigCG algorithm to non-symmetric linear systems with multiple right-hand sides

Understand

For Hermitian positive definite linear systems and eigenvalue problems, the eigCG algorithm is a memory efficient algorithm that solves the linear system and simultaneously computes some of its eigenvalues.

• The algorithm is based on the Conjugate-Gradient (CG) algorithm, however, it uses only a window of the vectors generated by the CG algorithm to compute approximate eigenvalues.
• The number and accuracy of the eigenvectors can be increased by solving more right-hand sides.
• For Hermitian systems with multiple right-hand sides, the computed eigenvectors can be used to speed up the solution of subsequent systems.