๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the numerical solution of a nonlinear matrix equation in Markov chains

โœ Scribed by Chun-Hua Guo

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
786 KB
Volume
288
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

โœฆ Synopsis

We consider iterative methods for t;le minimal nonnegativc :~oiu)i()n of the matrix equation G = ~, (), ,G', where the matrices ,4, are nonnegative and '~ ,)..I, is stocha:4ic. Convergence theory lbr an 'inversion frec algorithm is established. The convergence rale of this algorithm is sho,s'.i ~o be comparable with that of the I'~xstcst iteration among three fixed point iterations. ' ~i~

๐Ÿ“œ SIMILAR VOLUMES

On positive definite solution of a nonli
On positive definite solution of a nonlinear matrix equation
โœ Zhen-yun Peng; Salah M. El-Sayed ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 148 KB

## Abstract In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation __X__ + __A__^\*^__X__^โˆ’ฮฑ^__A__ = __Q__ with ฮฑ โˆˆ (0, โˆž) are given. Iterative methods to obtain the positive definite solutions are established and the rat