学术报告：李姣芬 教授（桂林电子科技大学）

主讲人：李姣芬 教授（桂林电子科技大学）

题目：Matrix Extrapolation Methods for Solving the Three-way IINDSCAL Problem from Multidimensional Scaling

时间：2025年5月24日上午10：50—11：20

地点：肇庆学院行政楼第二会议室

Abstract: Multidimensional scaling (MDS) is a dimensionality reduction technique that maps objects from a high-dimensional space to a low-dimensional one while preserving the pairwise distances between the objects. The individual differences scaling (INDSCAL) model is an extension of MDS that focuses on the differences between objects in the structure. In this talk, we explore the design and application of matrix extrapolation methods to solve the three-way INDSCAL model fitting problem. Building on the principles of vector polynomial extrapolation, we introduce matrix extrapolation techniques, including M-MPE, M-RRE and M-MMPE. We provide a comprehensive description of the acceleration principles and implementation steps for these methods, which are applied to matrix sequences generated by fixed-point iteration used to solve the three-way INDSCAL problem. Unlike traditional vector extrapolation methods for matrix sequences, our approach eliminates the need for vectorization operators. Extensive numerical experiments show that matrix extrapolation accelerates convergence significantly compared to the original fixed-point iteration sequence. Furthermore, the matrix extrapolation-based fixed-point iteration acceleration algorithm demonstrates a notable reduction in iteration time compared to existing solvers for the three-way INDSCAL problem.

报告人简介:李姣芬，桂林电子科技大学教授，博士生导师。曾访问美国南伊利诺伊大学、澳门大学等，研究方向数值代数及其应用。主持在研或完成国家自然科学基金项目4项。研究成果获广西自然科学奖二等奖和三等奖。 近年来以第一作者在IMA J Numer Anal., Adv.Comput.Math., J Sci.Comput.，BIT, Comput. Optim.Appl.等发表论文50余篇。