NEWTON'S METHOD FOR ZERO POINTS OF A MATRIX FUNCTION AND ITS APPLICATIONS TO QUEUEING MODELS

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概要

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• Let R(z) be a matrix function. We propose modified Newton's method to calculate zero points of det R(z). By the modified method, we can obtain accurate zero points by simple iterations. We also extend this problem to a multivariable case. Applications to the spectral analysis of M/G/1 type Markov chains are discussed. Important characteristics of these chains, e.g., the boundary vector and the matrix G, can be derived from zero points of a matrix function and corresponding null vectors. Numerical results are shown.

• 社団法人日本オペレーションズ・リサーチ学会の論文

著者

• Nishimura Shoichi

  Department Of Applied Mathematics Faculty Of Science Science University Of Tokyo

• Harashima Atsushi

  Mitsuba Co.

• Harashima A

  Meikai Univ. School Of Dentistry Saitama Jpn

関連論文

• NEWTON'S METHOD FOR ZERO POINTS OF A MATRIX FUNCTION AND ITS APPLICATIONS TO QUEUEING MODELS
• A QUEUEING SYSTEM WITH A SETUP TIME FOR SWITCHING OF THE SERVICE DISTRIBUTION
• Random Collision Processes with Transition Probabilities Belonging to the Same Type of Distribution
• An Inequality for a Metric in Random Collision Process
• EIGENVALUE EXPRESSION FOR A BATCH MARKOVIAN ARRIVAL PROCESS

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