A method for finding zeros of polynomial equations using a contour integral based eigensolver

Authors:
Tetsuya Sakurai;Junko Asakura;Hiroto Tadano;Tsutomu Ikegami;Kinji Kimura
Affiliations:
University of Tsukuba, Tsukuba, Japan;Square Enix Co. Ltd., Tokyo, Japan;University of Tsukuba, Tsukuba, Japan;AIST, Tsukuba, Japan;Kyoto University, Kyoto, Japan
Venue:
Proceedings of the 2009 conference on Symbolic numeric computation
Year:
2009

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Abstract

In this paper, we present a method for finding zeros of polynomial equations in a given domain. We apply a numerical eigensolver using contour integral for a polynomial eigenvalue problem that is derived from polynomial equations. The Dixon resultant is used to derive the matrix polynomial of which eigenvalues involve roots of the polynomial equations with respect to one variable. The matrix polynomial obtained by the Dixon resultant is sometimes singular. By applying the singular value decomposition for a matrix which appears in the eigensolver, we can obtain the roots of given polynomial systems. Experimental results demonstrate the efficiency of the proposed method.