A Successive over Relaxation Implicit Iterative Algorithm for Solving Stochastic Linear Systems with Markov Jumps

Tianrui Wu, Peiqi Huang () and Hong Chen
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Tianrui Wu: School of Science, Nanjing Forestry University, Nanjing 210037, China
Peiqi Huang: School of Science, Nanjing Forestry University, Nanjing 210037, China
Hong Chen: School of Science, Nanjing Forestry University, Nanjing 210037, China

Mathematics, 2024, vol. 12, issue 7, 1-14

Abstract: In order to solve continuous stochastic Lyapunov equations, a novel implicit iterative algorithm is presented by means of successive over relaxation (SOR) iteration in this article. Throughout this method, three tuning parameters are added for the improvement of the convergence rate. It is shown that this algorithm is monotonically bounded, and the convergence condition is also given and extended. Applying the latest updated estimates, this algorithm can attain a better convergence performance compared with other existing iterative algorithms when choosing appropriate tuning parameters. Finally, a numerical example is provided to illustrate the feasibility and priority of this approach.

Keywords: iterative algorithms; SOR; continuous stochastic Lyapunov equations; Markov jumps (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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