On Local Quadratic Convergence of Inexact Simplified Jacobi-Davidson Method

报告题目： On Local Quadratic Convergence of Inexact Simplified Jacobi-Davidson Method

报告人：白中治

报告时间：2017年9月29日15:00-16:00

报告地点：数学学院A302

主办单位：中国矿业大学数学学院

报告摘要：

Abstract: For the Hermitian eigenproblems, we prove local quadratic convergence of the inexact simplified Jacobi-Davidson method when the involved relaxed correction equation is solved by a standard Krylov subspace iteration. This method then shows local cubic convergence rate when the relaxed correction equation is solved to a prescribed precision proportional to the norm of the current residual. As a by-product, we obtain local cubic convergence of the simplified Jacobi-Davidson method. These results significantly improve the existing ones that show only local linear convergence for the inexact simplified Jacobi-Davidson method, which lead to local quadratic convergence for the simplified Jacobi-Davidson method when the tolerance of the inexact solve is particularly set to be zero. Numerical experiments confirm these theoretical results.

白中治教授简介：

白中治, 中国科学院数学与系统科学研究院研究员，曾任科学与工程计算国家重点实验室副主任。获得国家杰出青年科学基金，入选新世纪百千万人才工程计划（国家级人选），获得中国计算数学冯康奖、国家教育委员会科学技术进步奖、中国科学院青年科学家奖二、三等奖等。国务院政府特殊津贴获得者，国际线性代数学会会员，中国线性代数专业委员会委员。主要从事线性与非线性数值代数，并行算法及其应用，数值最优化方法与理论，微分代数方程组的数值方法，数值偏微分方程等方面的研究。