Mathematics Colloquium

Speaker: Xiaobing H. Feng from The University of Tennessee

Title: Reinventing Computational Mathematics/Methods for High-Dimensional Scientific Computing

Abstract:

The basic topics of computational mathematics include interpolation, approximation, numerical differentiation and integration, numerical ODEs and PDEs, optimization, and numerical linear algebra. Classical numerical methods and algorithms were developed for low-dimensional scientific and engineering problems because we humans 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.