Efficient Computation of the Characteristic Polynomial of a Polynomial Matrix

スポンサーリンク

概要

• 論文の詳細を見る

• This paper presents an efficient algorithm to compute the characteristic polynomial of a polynomial matrix. We impose the following condition on given polynomial matrix M. Let M_0 be the constant part of M, i.e. M_0≡M (mod (y, …, z)), where y, …, z are indeterminates in M. Then, all eigenvalues of M_0 must be distinct. In this case, the minimal polynomial of M and the characteristic polynomial of M agree, i.e. the characteristic polynomial f(x, y, …, z)=|xE - M| is the minimal degree (w.r.t. x) polynomial satisfying f(M, y, …, z)=0. We use this fact to compute f(x, y, …, z). More concretely, we determine the coefficients of f(x, y, …, z) little by little with basic matrix operations, which makes the algorithm quite efficient. Numerical experiments are given to compare the algorithm with conventional ones.

• 社団法人電子情報通信学会の論文
• 1999-05-25

著者

• Kitamoto Takuya

  Faculty Of Education Yamaguchi University

• Kitamoto Takuya

  Faculty Of Institutes Of Mathematics Univ. Of Tsukuba:(present) Department Of Education Yamaguchi Un

関連論文

• The Optimal H_∞ Norm of a Parametric System Achievable by an Output Feedback Controller
• On the Check of Accuracy of the Coefficients of Formal Power Series
• The Optimal H_∞ Norm of a Parametric System Achievable Using a Static Feedback Controller(Systems and Control)
• Extension of the Algorithm to Compute H_∞ Norm of a Parametric System
• Efficient Computation of the Characteristic Polynomial of a Polynomial Matrix
• On Efficient Computations of Approximate Roots
• Accurate Computation of a High Degree Coefficient of a Power Series Root(Algorithms and Data Structures)
• On Computation of Approximate Eigenvalues and Eigenvectors
• On Computation of a Power Series Root with Arbitrary Degree of Convergence
• Computation of the Peak of Time Response in the Form of Formal Power Series(Systems and Control)

スポンサーリンク