Symbolic-Numeric Algorithms for Verified Computations
Numerical computation is fast and has been widely used for solving various practical problems. However, it can not guarantee to give a complete set of verified solutions. Symbolic computation can provide entire validated solutions for many problems arising from science and industry, but some symbolic algorithms have double exponential complexity and therefore can only be used to solve small size problems. Symbolic-numeric hybrid computation aims to combine and integrate symbolic computation and numeric computation effectively to produce efficient and error-controllable algorithms for finding entire validated solutions. I will introduce several symbolic-numeric algorithms for finding valified solutions of (semi-)algebra problems.
Lihong Zhi received the B.S. degree in mathematics from Peking University and the Ph.D. degree in computer algebra from the Institute of Systems Science, Academia Sinica, Beijing, China. She is a professor of the Chinese Academy of Mathematics and Systems Science from 2009. She is involved in researches concerning validated (certified) outputs via algebraic and exact techniques, error estimation, interval techniques or global optimization strategies.