A convex dual programming for the rational minimax approximation and Lawson’s iteration

江蘇省應用數學（中國礦業大學）中心系列學術報告

報告題目：A convex dual programming for the rational minimax approximation and Lawson’s iteration

報告人：張雷洪 教授 (蘇州大學 數學科學學院)

報告時間：2024年4月21日（周日）上午10:00-11:00

報告地點：伟德bvB303

報告摘要：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 paper, we propose 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.

報告人簡介：張雷洪，2008年博士畢業于香港浸會大學，現為蘇州大學數學科學學院教授。從事最優化理論與計算，數值線性代數，數值逼近，數據挖掘等領域的研究。曾赴美國北卡羅來納州立大學、美國德克薩斯大學阿靈頓分校等進行訪問。獲中國數學會計算數學分會的第四屆“應用數值代數獎”， 2018 年和 2019 年兩屆“世界華人數學家聯盟最佳論文獎-若琳獎”，2019 年上海市自然科學三等獎(第一完成人)。 成果發表在包括SIAM系列雜志,及《Math. Progam.》、《Math. Comp.》、《Numer. Math.》、《IEEE Trans. Pattern Anal. Mach. Intell.》等。主持多項國家自科項目,參與國家重大研究計劃。目前任SCI雜志《Operators and Matrices》，ESCI期刊《Numerical Algebra, Control and Optimization》，《計算數學》編委等。