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- Erich Kaltofen, Zhengfeng Yang, Lihong Zhi
- ISSAC
- 2006

We consider the problem of computing minimal real or complex deformations to the coefficients in a list of relatively prime real or complex multivariate polynomials such that the deformed polynomialsâ€¦ (More)

- Robert M. Corless, Stephen M. Watt, Lihong Zhi
- IEEE Transactions on Signal Processing
- 2004

We present a stable and practical algorithm that uses QR factors of the Sylvester matrix to compute the greatest common divisor (GCD) of univariate approximate polynomials over /spl Ropf/[x] or /splâ€¦ (More)

The task of determining the approximate greatest common divisor (GCD) of univariate polynomials with inexact coefficients can be formulated as computing for a given Sylvester matrix a new Sylvesterâ€¦ (More)

- Lihong Zhi, Greg J. Reid
- 2004

Consider a general polynomial system S in x1, . . . , xn of degree q and its corresponding vector of monomials of degree less than or equal to q. The system can be written as M0 Â· [xq1, xqâˆ’1 1 x2, .â€¦ (More)

- Erich Kaltofen, Bin Li, Zhengfeng Yang, Lihong Zhi
- ISSAC
- 2008

We generalize the technique by Peyrl and Parillo [Proc. SNC 2007] to computing lower bound certificates for several well-known factorization problems in hybrid symbolic-numeric computation. The ideaâ€¦ (More)

- Gregory J. Reid, Lihong Zhi
- J. Symb. Comput.
- 2009

We briefly survey several existing methods for solving polynomial system with inexact coefficients, then introduce our new symbolic-numeric method which is based on the geometric (Jet) theory ofâ€¦ (More)

- Joe Bonasia, FranÃ§ois Lemaire, Greg J. Reid, Lihong Zhi, Lihong Zhi
- 2003

There has been considerable progress in the theory and computer implementation of symbolic computation algorithms to automatically determine and exploit exact symmetries of exact differentialâ€¦ (More)

The problem of approximating the greatest common divisor(GCD) for polynomials with inexact coefficients can be formulated as a low rank approximation problem with a Sylvester matrix. In this paper,â€¦ (More)

- Shuhong Gao, Erich Kaltofen, John May, Zhengfeng Yang, Lihong Zhi
- ISSAC
- 2004

The input to our algorithm is a multivariate polynomial, whose complex rational coefficients are considered imprecise with an unknown error that causes f to be irreducible over the complex numbers C.â€¦ (More)

- Erich Kaltofen, John P. May, Zhengfeng Yang, Lihong Zhi
- J. Symb. Comput.
- 2008

We describe the design, implementation and experimental evaluation of new algorithms for computing the approximate factorization of multivariate polynomials with complex coefficients that containâ€¦ (More)