Computation of an exact GCRD of several polynomial matrices: QR decomposition approach

IF 1 3区 数学 Q1 MATHEMATICS
Anjali Beniwal , Tanay Saha , Swanand R. Khare
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Abstract

This paper addresses the problem of computing an exact Greatest Common Right Divisor (GCRD) of several univariate polynomial matrices B1(s),,Bt(s). We construct a polynomial matrix P(s) by stacking B1(s),,Bt(s), one below the other. This results in P(s) being wide, square or tall, each examined individually. We further prove the equivalence of rank deficiency of a particular generalized Sylvester matrix associated with P(s) to the degree of the determinant of a GCRD of B1(s),,Bt(s) when P(s) is a tall matrix with full normal rank. This equivalence enables us to propose a method to extract a GCRD based on the ‘effectively eliminating’ QR (EEQR) decomposition of that generalized Sylvester matrix. We also propose a computationally efficient algorithm to extract the exact GCRD. To validate the theoretical findings, we provide several numerical examples.
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来源期刊
CiteScore
2.20
自引率
9.10%
发文量
333
审稿时长
13.8 months
期刊介绍: Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
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