Displacement structure: theory and applications
SIAM Review
SIAM Review
Total Least Norm Formulation and Solution for Structured Problems
SIAM Journal on Matrix Analysis and Applications
Approximate polynomial greatest common divisors and nearest singular polynomials
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Optimization strategies for the approximate GCD problem
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Efficient algorithms for computing the nearest polynomial with constrained roots
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Structured Total Least Norm for Nonlinear Problems
SIAM Journal on Matrix Analysis and Applications
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Journal of Symbolic Computation
Approximate factorization of multivariate polynomials via differential equations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
The approximate GCD of inexact polynomials
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
SIAM Journal on Optimization
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
On exact and approximate interpolation of sparse rational functions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Exact polynomial factorization by approximate high degree algebraic numbers
Proceedings of the 2009 conference on Symbolic numeric computation
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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 symbolic-numeric algorithms based on Gauss-Newton iteration, structured total least squares (STLS), semide finite programming and other numeric optimization methods.