A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part
A class of nested splitting conjugate gradient (NSCG) methods is proposed for solving large sparse systems of linear equations with coefficient matrices with a dominant symmetric positive definite part. The NSCG method is actually an inner/outer iterative method with a particular splitting iteration as its outer iteration, and with the CG iteration as its inner iteration. The inner CG iteration itself can be further preconditioned by employing a suitable preconditioner. This naturally leads to a preconditioned NSCG (PNSCG) method. Numerical examples show that NSCG and PNSCG converge faster and more robustly to the exact solution than the generalized minimal residual (GMRES) method and its preconditioned variant, respectively.
scientific article; zbMATH DE number 2085902