A Newton-type method for two-dimensional eigenvalue problems

：苏仰锋（复旦大学）
：2022-06-18 09:00
：腾讯会议ID：136-774-875（无密码）

报告人：苏仰锋（复旦大学）

时  间：6月18日上午09:00

地  点：腾讯会议ID：136-774-875（无密码）

内容摘要:

Two-dimensional eigenvalue problems (2DEVP) equations in complex Hermitian case contain complex quadratic forms which is non-holomorphic. In this case, standard Newton method fails to apply. An existing strategy to solve this problem is to transform them into real problems (TRN). However, this method doubles the size of equations and thus is time consuming. On the other hand, the non-isolation of the solution set in 2DEVP also complicates the analysis. We propose a Newton type method which solves the problem caused by non-holomophism and non-isolation. It has locally quadratic convergence rate and is about at least twice as much efficient as TRN. We hope our ideas can provide insights for solving other problems including non-holomorphism and non-isolation. We apply our algorithm to calculate the distance to instability. Numerical experiments show its advantages in efficiency while keeping good convergence compared with the current state of art algorithms.

个人简介：

苏仰锋，复旦大学数学科学学院教授，上海数学中心谷超豪研究所长聘教授。曾任计算数学系系主任、中国数学会计算数学分会常务理事等。主持国家自然科学基金多项，包括重大研究计划中的重点项目。2006年度上海市曙光人才，2012年上海市自然科学奖一等奖（第一完成人）。研究兴趣为数值代数，特别是特征值问题；集成电路电子设计自动化中的数值代数问题。

 

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