THE QUASI-MINIMAL RESIDUAL ALGORITHM APPLIED TO COMPLEX SYMMETRICAL LINEAR-SYSTEMS IN QUANTUM REACTIVE SCATTERING

The solution of systems of linear equations Ax=b with complex symmetri c coefficient matrix A of size N, typically appearing in quantum-react ive scattering problems, is discussed. The quasiminimal residual (QMR) method is introduced to solve the complex symmetric linear system and is compared to the generalized minimal residual (GMRES) method. The m ethods are applied to two different chemical problems: the initial sta te-selected reaction probability for the H-2+OH-->H +H2O reaction, and the cumulative reaction probability for the isomerization of ketene, both with N>10(4). It is shown that the QMR method behaves more favora bly, i.e., converges faster, than the GMRES for large N, especially wh en high accuracy is needed. (C) 1995 American Institute of Physics.