ON A DIRECT METHOD FOR THE SOLUTION OF NEARLY UNCOUPLED MARKOV-CHAINS

被引：15

作者：

STEWART, GW ^{[1
]}

ZHANG, G ^{[1
]}

机构：

[1] UNIV MARYLAND,INST ADV COMP STUDIES,COLLEGE PK,MD 20742

来源：

NUMERISCHE MATHEMATIK | 1991年 / 59卷 / 01期

关键词：

D O I：

10.1007/BF01385767

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1 / 11

页数：11

共 11 条

[1] ON THE SMALLEST POSITIVE SINGULAR VALUE OF A SINGULAR M-MATRIX WITH APPLICATIONS TO ERGODIC MARKOV-CHAINS [J].

BARLOW, JL .

SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1986, 7 (03) :414-424

[2]

Berman A, 1979, MATH SCI CLASSICS AP, V9, DOI DOI 10.1137/1.9781611971262

[3] SOLUTION OF HOMOGENEOUS SYSTEMS OF LINEAR-EQUATIONS ARISING FROM COMPARTMENTAL-MODELS [J].

FUNDERLIC, RE ;

MANKIN, JB .

SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1981, 2 (04) :375-383

[4]

FUNDERLIC RE, 1981, LINEAR ALGEBRA APPL, V44, P99

[5] REGENERATIVE ANALYSIS AND STEADY-STATE DISTRIBUTIONS FOR MARKOV-CHAINS [J].

GRASSMANN, WK ;

TAKSAR, MI ;

HEYMAN, DP .

OPERATIONS RESEARCH, 1985, 33 (05) :1107-1116

[6] COMPARISON OF SOME DIRECT METHODS FOR COMPUTING STATIONARY DISTRIBUTIONS OF MARKOV-CHAINS [J].

HARROD, WJ ;

PLEMMONS, RJ .

SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1984, 5 (02) :453-469

[7] COMPUTABLE ERROR-BOUNDS FOR AGGREGATED MARKOV-CHAINS [J].

STEWART, GW .

JOURNAL OF THE ACM, 1983, 30 (02) :271-285

[8]

STEWART GW, 1990, CSTR2406 U MAR DEP C

[9]

Stewart GW, 1973, INTRO MATRIX COMPUTA

[10]

Wilkinson JH., 1965, ALGEBRAIC EIGENVALUE

← 1 2 →