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

摘要

The solution of systems of linear equations Ax=b with complex symmetric coefficient matrix A of size N, typically appearing in quantum-reactive 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 methods are applied to two different chemical problems: the initial state-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 favorably, i.e., converges faster, than the GMRES for large N, especially when high accuracy is needed. (C) 1995 American Institute of Physics. [References: 21]