On a direct method for the solution of nearly uncoupled Markov chains (Q911215)
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scientific article; zbMATH DE number 4143331
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a direct method for the solution of nearly uncoupled Markov chains |
scientific article; zbMATH DE number 4143331 |
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On a direct method for the solution of nearly uncoupled Markov chains (English)
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1991
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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 associate with aggregation and the coupling respectively.
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nearly uncoupled Markov chains
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direct method
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LU decomposition
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Gaussian elimination
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rounding errors
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diagonal pivoting
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condition numbers
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