On a direct method for the solution of nearly uncoupled Markov chains | Zendy

G. W. Stewart | Zendy; G. Zhang | Zendy

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On a direct method for the solution of nearly uncoupled Markov chains

Author(s) -

G. W. Stewart,

G. Zhang

Publication year - 1991

Publication title -

numerische mathematik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.214

H-Index - 90

eISSN - 0945-3245

pISSN - 0029-599X

DOI - 10.1007/bf01385767

Subject(s) - mathematics , markov chain , diagonal , gaussian elimination , gaussian , rounding , coupling (piping) , numerical analysis , mathematical analysis , computational chemistry , statistics , chemistry , computer science , geometry , mechanical engineering , engineering , operating system

This note is concerned with the accuracy of the solution of nearly uncoupled Markov chains by a direct method based on the LU decomposition. It is shown that plain Gaussian elimination may fail in the presence of rounding errors. A modification of Gaussian elimination with diagonal pivoting and correction of small pivots is proposed and analyzed. It is shown that the accuracy of the solution is affected by two condition numbers associated with aggregation and the coupling respectively.

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