Abstract: The basic topics of computational mathematics often include interpolation, approximation, numerical differentiation and integration, numerical ordinary differential equations and partial differential equations (PDEs), optimization, and numerical linear algebra. Classical numerical methods and algorithms were developed for low-dimensional (d=1,2,3) scientific problems because we live in a 3-dimensional (or 4-dimensional if spacetime is considered) world. However, recent advances in image processing, financial math, data science, neural networks, and machine learning require solving the above-mentioned problems in much higher dimensions. Because of the Curse of Dimensionality (CoD), the classical numerical methods and algorithms become inefficient and/or impractical and/or infeasible for solving those high-dimensional problems. In this talk, I shall use high-dimensional numerical integration and numerical PDEs as examples to present some recent approaches and advances in developing efficient computational methods and algorithms for these two classes of high-dimensional scientific computational problems.
Speaker’s Bio: Xiaobing Feng is a professor and chair of the Department of Mathematics at the University of Tennessee. Xiaobing received his PhD in 1992 from Purdue University under the advisement of Dr. Jim Douglas. His research interests include high-dimensional computation and analysis/numerical methods of the following: nonlinear PDEs, stochastic PDEs, fractional calculus, and nonlocal differential equations.
Last Updated: January 25, 2024 - 1:40 pm