On Efficient Computations of Approximate Roots

スポンサーリンク

概要

• 論文の詳細を見る

• Given a multivariate polynomial f(x,y) in variables x,y, root g(y) of f(x,y)=0 with respect to x can be expanded in the form of g(y)=α_0+α_1y+・・・+α_ky^k+・・・ as Taylor series. The series truncated at k-th degree in y is called k-th approximate root. It is known that approximate roots can be computed with symbolic Newton's method efficiently. In this paper, we present a more efficient version of the symbolic Newton's method. More concretely, first, we introduce the method proposed by M. Shaw and J.F. Traub, with which we can improve conventional symbolic Newton's method. Then, we further improve the symbolic Newton's method, adding some modifications to M. Shaw and J.F. Traub's method. We show efficiency of our method, performing both of complexity analysis and numerical experiments.

• 社団法人電子情報通信学会の論文
• 2002-02-01

著者

• Kitamoto Takuya

  Faculty Of Education Yamaguchi University

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