On a conjugate gradient-type method for solving complex symmetric linear systems

摘要

We consider large sparse linear systems Ax = b with complex symmetric coefficient matrices A = A~T which arise, e.g., from the discretization of partial differential equations with complex coefficients. For the solution of such systems we present a new conjugate gradient-type iterative method, CSYM, which is based on unitary equivalence transformations of A to symmetric tridiagonal form. An analysis of CSYM shows that its convergence depends on the singular values of A and that it has both, the minimal residual property and constant costs per iteration step. We compare the algorithm with other methods for solving large sparse complex symmetric systems.