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Published in:
2015 | OriginalPaper | Chapter
On the Relation Between Matrices and the Greatest Common Divisor of Polynomials
Author : Nikolai L. Manev
Published in: Large-Scale Scientific Computing
Publisher: Springer International Publishing
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Abstract
Following the Barnett’s approach to gcd(a(x),b(x)) based on the use of companion matrix we develop an extended algorithm that gives effectively \(d(x),\ u(x),\ v(x),\ a_1(x)\) and \(b_1(x)\), where \(a_1(x)=a(x)/d(x), b_1(x)=b(x)/d(x)\) and \(d(x)=u(x)a(x)+v(x)b(x).\) The algorithm is suitable for parallel realization on GPU, FPGA, and smart cards.