报告题目：A convex dual programming for the rational minimax approximation and Lawson's iteration

报 告 人：张雷洪（苏州大学）

报告时间：2024年7月23日  16:00-17:00

报告地点：格物楼528

报告摘要：

Computing the discrete rational minimax approximation in the complex plane is challenging. Apart from Ruttan's sufficient condition, there are few other sufficient conditions for global optimality. The state-of-the-art rational approximation algorithms, such as the adaptive Antoulas-Anderson(AAA), AAA-Lawson, and the rational Krylov fitting (RKFIT) method, perform highly efficiently, but the computed rational approximants may be near-best. In this talk, we will introduce a convex programming approach, the solution of which is guaranteed to be the rational minimax approximation under Ruttan's sufficient condition. Furthermore, we present a new version of Lawson's iteration for solving this convex programming problem. The computed solution can be easily verified as the rational minimax approximant. We show that this updated version of Lawson's iteration converges monotonically with respect to the objective function of the convex programming. It is an effective competitive approach for the rational minimax problem, compared to the highly efficient AAA, AAA-Lawson, and the stabilized Sanathanan-Koerner iteration.

报告人简介：

张雷洪，2008年博士毕业于香港浸会大学，现为苏州大学数学科学学院教授。研究方向为最优化理论与计算、数值线性代数、数据科学等。主持多项自然青年/面上项目，参与国家自然科学基金重大研究计划。在SIOPT、SIMAX、SISC、Math. Comput.、Numer. Math.、IEEE TPMAI等期刊已发表50多篇学术论文。曾获第四届中国数学会计算数学分会“应用数值代数奖”、上海财经大学第四届学术奖、2018和2019年世界华人数学家联盟最佳论文奖（若琳奖），及2019年上海市自然科学三等奖（第一完成人）等。现为学术杂志《Operators and Matrices》和《Numerical Algebra, Control and Optimization》编委。