Solution of Non-symmetric Linear Systems by Bi-conjugate Gradients or Conjugate Gradients Squared

摘要

An important problem of numerical linear algebra is the solution of a set of linear equations Ax = b were A is a regular coefficient matrix. In the report the method of bi-conjugate gradients (bi-cg method) and the method of conjugate gradients squared (cgs method) are used to solve such systems. A necessary and sufficient condition is given in order that a given number of iterations of both methods is executable. Subsequently the preconditioned bi-cg and cgs methods are considered with an incomplete LU sup T-decomposition as preconditioning. Numerical experiments on three model problems for the convection-diffusion equation are discussed. At the end of the report, the listings of the Fortran routines BCG, CGS, BCGEIS and CGSEIS are given.