On a conjugate gradient-type method for solving complex symmetric linear systems
The authors present a new conjugate gradient-type iterative method (CSYM) for solving large sparse systems of linear equations with complex coefficient matrices. The method is based on unitary equivalence transformations of the coefficient matrix to complex symmetric tridiagonal form. The procedure used in the algorithm is similar to the procedure applied in the well known Lanczos method. One can find an excellent description of the new technique with theoretical part, comparison with two often used algorithms (CGNR and QMR) by some theoretical investigations as well as by numerical examples which are well chosen and representative. The new algorithm is analyzed and some theoretical statements are given. It is shown that it is fundamentally different from Krylov subspace methods when the original complex symmetric problem is reformulated as a real problem of twice the dimension. The numerical results which are shown in the figures of the paper give a good impression about the performance of all three methods even if they are used without preconditioning.
conjugate gradient-type iterative method
large sparse systems of linear equations
scientific article; zbMATH DE number 1331748
scientific article