Convergence of nested iterative methods for symmetric P-regular splittings

摘要

We study the convergence of nested iterative methods and present conditions on the splittings corresponding to the iterative methods to guarantee convergence for any number of the inner iterations. In contrast to Lanzkron, Rose, and Szyld [Numer. Math., 58 (1991), pp. 685-702], Frommer and Szyld [Numer. Math., 63 (1992), pp. 345-356; Numer. Math., 69 (1994), pp. 141-153], and Cao [ Math. Numer. Sinica, 17 (1995), pp. 98-109; Linear Algebra Appl., 22 (1995), pp. 159-170], in which the coefficient matrices are either of monotone matrices or of H-matrices and the splittings they set relate to regular and weak regular ones, the coefficient matrices considered in this paper are symmetric positive definite and the splittings we set relate to P-regular ones. [References: 9]