CONVERGENCE ANALYSIS ON ITERATIVE METHODS FOR SEMIDEFINITE SYSTEMS

• 来源期刊: 计算数学(英文版)
• 关键词: Semidefinite systems Subspace correction methods Iterative methods Energy norm convergence
• 年，卷（期）: 2008,（6）
• 页码范围: 797-815
• 页数: 19页
• 语种: 英文

摘要

The convergence analysis on the general iterative methods for the symmetric and pos-itive semidefinite problems is presented in this paper. First, formulated are refined neces-sary and sufficient conditions for the energy norm convergence for iterative methods. Some illustrative examples for the conditions are also provided. The sharp convergence rate iden-tity for the Gauss-Seidel method for the semidefinite system is obtained relying only on the pure matrix manipulations which guides us to obtain the convergence rate identity for the general successive subspace correction methods. The convergence rate identity for the successive subspace correction methods is obtained under the new conditions that the local correction schemes possess the local energy norm convergence. A convergence rate estimate is then derived in terms of the exact subspace solvers and the parameters that appear in the conditions. The uniform convergence of multigrid method for a model prob-lem is proved by the convergence rate identity. The work can be regraded as unified and simplified analysis on the convergence of iteration methods for semidefinite problems [8,9].