主 题：Chebfun - From Function Approximations to Solution of Differential Equations
主讲人：英国牛津大学数学系 徐宽 博士后
Dr. Kuan Xu obtained his Ph.D. from New Jersey Institute of Technology and Rutgers, the State University of New Jersey at Newark. Before joining the Numerical Analysis Group at Oxford University in UK where he is now a postdoctoral research fellow in the Chebfun team, he served as algorithm scientist in the Real-Time Optimization and Controls Laboratory at General Electric Global Research in the state of New York, US.
Chebfun is a collection of algorithms and an open-source software system in object-oriented MATLAB which extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions, giving users the feel of symbolic computing but with the lightning speed of numerical computation. It handles function approximations along with further operations based on these approximations with ease. Chebfun is also powerful in solving differential equations offering users its speed, accuracy and robustness.
In this talk, we will first discuss the mathematical basis of the system - combinations of the state-of-the-art tools for function approximations - Chebyshev expansions, fast Fourier transform, barycentric interpolation, recursive zerofinding, etc. Then we will explore Chebfun's capability on solving differential equations by focusing on boundary values problems in 1D with the help of Chebgui, a graphical user interface to Chebfun's capabilities for solving ODEs and PDEs.
This talk will be concluded by a remark on a potential direction of numerical analysis in future.