Kazuki Kondo
Abstract
For the problem of sparse interpolation of multivariate polynomials, we propose robust computation methods based on the modified numerical Ben-Or/Tiwari algorithm by M. Giesbrecht, G. Labahn, and W.-s. Lee.
- M. Ben-Or and P. Tiwari. A deterministic algorithm for sparse multivariate polynomial interpolation. In Proc. Twentieth Annual ACM Symp. Theory Comput. (STOC1988), 301--309, 1988.Google Scholar
Digital Library
- M. Giesbrecht, G. Labahn, and W.-s. Lee. Symbolic-numeric sparse interpolation of multivariate polynomials. J. Symbolic Comput., 44:943--959, 2009.Google ScholarDigital Library
- E. L. Kaltofen, W.-s. Lee, and Z. Yang. Fast estimates of Hankel matrix condition numbers and numeric sparse interpolation. In Proc. 2011 Internat. Workshop Symb.-Numer. Comput. (SNC'2011), 130--136, 2011.Google ScholarDigital Library
- D. Numahata and H. Sekigawa. Robust algorithms for sparse interpolation of multivariate polynomials. ACM Communications in Computer Algebra, 52(4):145--147, 2018.Google ScholarDigital Library
Index Terms
- Robust computation methods for sparse interpolation of multivariate polynomials
Recommendations
Sparse multivariate polynomial interpolation on the basis of Schubert polynomials
Schubert polynomials were discovered by A. Lascoux and M. Schützenberger in the study of cohomology rings of flag manifolds in 1980s. These polynomials generalize Schur polynomials and form a linear basis of multivariate polynomials. In 2003, Lenart and ...
Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials
AbstractSparse interpolation refers to the exact recovery of a function as a short linear combination of basis functions from a limited number of evaluations. For multivariate functions, the case of the monomial basis is well studied, as is now the basis ...
Computation of GCD of Sparse Multivariate Polynomials by Extended Hensel Construction
SYNASC '15: Proceedings of the 2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)Let F(x, u1, , ul) be a squarefree multivariate polynomial in main variable x and sub-variables u1, , ul. We say that the leading coefficient (LC) of F is singular if it vanishes at the origin of sub-variables. A representative algorithm for nonsparse ...
Comments