On a Direct Method for the Solution ofNearly Uncoupled Markov
نویسنده
چکیده
abstract 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 modiication of Gaussian elimination with diagonal pivoting as well as corrections of small pivots by sums of oo-diagonal elements in the pivoting columns is proposed and analyzed. It is shown that the accuracy of the solution is aaected by two condition numbers associate with the aggregate and the coupling respectively. ABSTRACT 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 modiication 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 aaected by two condition numbers associate with aggregation and the coupling respectively. Abbreviated Title. Solution of NUMCs.
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