𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A class of iteration methods based on the moser formula for nonlinear equations in Markov chains

✍ Scribed by Zhong-Zhi Bai

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
945 KB
Volume
266
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

Many stochastic models in queueing, inventory, communications, and dam theories, etc., result in the problem of numerically determining the minimal nonnegative solutions for a class of nonlinear matrix equations. Various iterative methods have been proposed to determine the matrices of interest. We propose a new, efficient successive-substitution Moser method and a Newton-Moser method which use the Moser formula (which, originally, is just the Schulz method). These new methods avoid the inverses of the matrices, and thus considerable savings on the computational workloads may be achieved. Moreover, they are much more suitable for implementing on parallel multiprocessor systems. Under certain conditions, we establish monotone convergence of these new methods, and prove local linear convergence for the substitution Moser method and superlinear convergence for the Newton-Moser method.

πŸ“œ SIMILAR VOLUMES

On the numerical solution of a nonlinear
On the numerical solution of a nonlinear matrix equation in Markov chains
✍ Chun-Hua Guo πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 786 KB

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

A three-dimensional finite volume method
A three-dimensional finite volume method based on radial basis functions for the accurate computational modelling of nonlinear diffusion equations
✍ T.J. Moroney; I.W. Turner πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 985 KB

We investigate the effectiveness of a finite volume method incorporating radial basis functions for simulating nonlinear diffusion processes. Past work conducted in two dimensions is extended to produce a three-dimensional discretisation that employs radial basis functions (RBFs) as a means of local