【摘要】 基于Givens-QR分解,给出了companion矩阵的一种伪谱定义和相应的快速计算方法;利用给出的companion矩阵伪谱作为工具分析了balance技术的作用,说明了balance技术在矩阵计算中的重要性和有效性;针对多项式零点扰动,探讨了companion矩阵的结构伪谱;最后,对文中所给算法进行了数值试验与比较,说明了其正确性和有效性.更多还原

【Abstract】 Based on the Givens-QR factorization,a fast algorithm for the pseudospectra of companion matrix was proposed.The balance technique was discussed using the pseudospectra as a tool.It is shown that the balance is important and efficient in the matrix computations.Also,the structured pseudospectra of companion matrix were discussed in order to analysize the perturbation of the zeros of polynomial.Finally,numerical experiments and comparisons were presented to illustrate the correctness and the effectiveness of the proposed results.更多还原