Average block nonlinear Kaczmarz method with adaptive momentum for nonlinear system

发布时间：2025-11-27 作者：浏览次数：

Speaker:	王冬岭	DateTime:	2025年11月28日（周五）下午16:30-18:00
Brief Introduction to Speaker: 王冬岭，湘潭大学教授，博士生导师；2013年6月博士毕业于湘潭大学计算数学专业。主要从事动力系统保结构算法、分数阶微分方程数值方法的研究，主持陕西省自科基金、国家自科基金天元基金、青年基金、面上项目；参加国家自科基金重点项目；多次到香港中文大学、北京计算科学研究中心、中国科学院数学与系统研究院等高校做访问学者；已在SIAM J. Numer. Anal., J. Comput. Phy., J. Sci. Comput.，BIT Numer. Math.等计算数学杂志发表论文四十余篇。		Place:	国交二号楼315会议室
Abstract:The Kaczmarz method has received significant attention as an efficient iterative algorithm for solving large-scale linear systems due to its simplicity and low memory requirements. However, progress in developing nonlinear Kaczmarz variants for solving nonlinear systems of substantial scale remains limited. This paper presents a novel class of momentum-accelerated averaging block nonlinear Kaczmarz methods designed to address large-scale nonlinear systems and ill-posed problems. Our main contribution is twofold: (1) We develop an adaptive parameter selection mechanism for step sizes and momentum coefficients, culminating in the proposed Average Block Nonlinear Kaczmarz Method with Adaptive Momentum (ABNKAm); The algorithm achieves exceptional computational efficiency requiring only minimal vector inner-product computations per iteration, resulting in dramatically reduced arithmetic complexity and memory footprint; (2) We provide rigorous theoretical convergence guarantees under mild...

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