MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIX EQUATION

• 来源期刊: 计算数学（英文版）
• 关键词: Quadratic matrix equation,Quadratic eigenvalue problem Solvent,Bernoulli's iteration,Newton's method,Local convergence
• 年，卷（期）: 2007,（5）
• 页码范围: 498-511
• 页数: 14页
• 语种: 英文

摘要

We construct a modified Bernoulli iteration method for solving the quadratic matrix equation AX2+BX+C=0,where A,B and C are square matrices.This method is motivated from the Gauss-Seidel iteration for solving linear systems and the ShermanMorrison-Woodbury formula for updating matrices.Under suitable conditions, we prove the local linear convergence of the Dew method.An algorithm is presented to find the solution of the quadratic matrix equation and some numerical results are given to show the feasibility and the effectiveness of the algorithm.In addition,we also describe and analyze the block version of the modified Bernoulli iteration method.