Numerical optimization in hybrid symbolic-numeric computation

Approximate symbolic computation problems can be formulated as constrained or unconstrained optimization problems, for example: GCD [3, 8, 12, 13, 23], factorization [5, 10], and polynomial system solving [2, 25, 29]. We exploit the special structure of these optimization problems, and show how to design efficient and stable hybrid symbolicnumeric algorithms based on Gauss-Newton iteration, structured total least squares (STLS), semidefinite programming and other numeric optimization methods. Categories and Subject Descriptors: I.2.1 [Computing Methodologies]: Symbolic and Algebraic Manipulation

• Type: Conference
• Year: 2007
• Where: ISSAC
• Authors: Lihong Zhi
• Keywords: ISSAC 2007, Optimization Problems, Symbolic Computation Problems, Unconstrained Optimization Problems