Computing Approximation GCD of Several Polynomials by Structured Total Least Norm

• 作者: Qingwen Wang Xinjun Zhang Xuefeng Duan
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: SYLVESTER Matrix Approximate GREATEST Common DIVISOR Low Rank APPROXIMATION STRUCTURED TOTAL Least Norm Numerical Method
• 年，卷（期）: 2013,（4）
• 页码范围: 39-46
• 页数: 8页
• 分类号: O1

摘要

The task of determining the greatest common divisors (GCD) for several polynomials which arises in image compression, computer algebra and speech encoding can be formulated as a low rank approximation problem with Sylvester matrix. This paper demonstrates a method based on structured total least norm (STLN) algorithm for matrices with Sylvester structure. We demonstrate the algorithm to compute an approximate GCD. Both the theoretical analysis and the computational results show that the method is feasible.