کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5776282 | 1631971 | 2017 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Inverse multivariate polynomial root-finding: Numerical implementations of the affine and projective Buchberger-Möller algorithm
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Inverse multivariate polynomial root-finding: Numerical implementations of the affine and projective Buchberger-Möller algorithm Inverse multivariate polynomial root-finding: Numerical implementations of the affine and projective Buchberger-Möller algorithm](/preview/png/5776282.png)
چکیده انگلیسی
We address the inverse problem of multivariate polynomial root-finding: given a finite set Z of points in Cn, find the minimal set of multivariate polynomials that vanish on Z. Two SVD-based algorithms are presented: one algorithm works only for affine roots and as a result almost always returns an overdetermined set of polynomials. This issue is resolved in the second algorithm by introducing projective points and hence adding roots at infinity. In addition, we show how the use of multiplicity structures is required to describe roots with multiplicities. We also derive a suitable tolerance that needs to be used when the roots are not known with infinite precision. A measure of how well the resulting polynomials vanish approximately on Z is shown to be the smallest singular value of a particular matrix. Both affine and projective implementations of our algorithm are applied to the problem of computing continuous-time polynomial dynamical systems from a given set of fixed points, demonstrating the effectiveness and robustness of our proposed methods.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 320, 15 August 2017, Pages 15-29
Journal: Journal of Computational and Applied Mathematics - Volume 320, 15 August 2017, Pages 15-29
نویسندگان
Kim Batselier, Ngai Wong,