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A Fast Newton-Shamanskii Iteration for a Matrix Equation Arising from MG1-Type Markov Chains
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-10-19
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
For the nonlinear matrix equations arising in the analysis of M/G/1-type and GI/M/1-type Markov chains, the minimal nonnegative solution G or R can be found by Newton-like methods.
We prove monotone convergence results for the Newton-Shamanskii iteration for this class of equations.
Starting with zero initial guess or some other suitable initial guess, the Newton-Shamanskii iteration provides a monotonically increasing sequence of nonnegative matrices converging to the minimal nonnegative solution.
A Schur decomposition method is used to accelerate the Newton-Shamanskii iteration.
Numerical examples illustrate the effectiveness of the Newton-Shamanskii iteration.
American Psychological Association (APA)
Guo, Pei-Chang. 2017. A Fast Newton-Shamanskii Iteration for a Matrix Equation Arising from MG1-Type Markov Chains. Mathematical Problems in Engineering،Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1190314
Modern Language Association (MLA)
Guo, Pei-Chang. A Fast Newton-Shamanskii Iteration for a Matrix Equation Arising from MG1-Type Markov Chains. Mathematical Problems in Engineering No. 2017 (2017), pp.1-8.
https://search.emarefa.net/detail/BIM-1190314
American Medical Association (AMA)
Guo, Pei-Chang. A Fast Newton-Shamanskii Iteration for a Matrix Equation Arising from MG1-Type Markov Chains. Mathematical Problems in Engineering. 2017. Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1190314
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1190314