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

• Nishimura Shoichi

  Department of Applied Mathematics, Faculty of Science, Science University of Tokyo

• Harashima Atsushi

  Mitsuba Co.

抄録

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.

収録刊行物

• 日本オペレーションズ・リサーチ学会論文誌

  日本オペレーションズ・リサーチ学会論文誌 43 (3), 396-416, 2000

  公益社団法人 日本オペレーションズ・リサーチ学会

キーワード

• Management Science and Operations Research
• General Decision Sciences

詳細情報

• CRID: 1390001204108660608
• NII論文ID: 110001183924
• NII書誌ID: AA00703935
• DOI: 10.15807/jorsj.43.396
• ISSN: 21888299
• ISSN: 04534514
• NDL書誌ID: 5520471
• Web Site: http://id.ndl.go.jp/bib/5520471
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I5520471
• Web Site: https://www.jstage.jst.go.jp/article/jorsj/43/3/43_KJ00001201993/_pdf
• 本文言語コード: en
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