Open AccessInversion free Iterative Method for Finding Symmetric Solution of the Nonlinear Matrix Equation πΏ β π¨βπΏππ¨ = π° (π β₯ π)
Author(s) -
Chacha Stephen Chacha
Publication year - 2021
Publication title -
tanzania journal of science/tanzania journal of science
Language(s) - English
Resource type - Journals
eISSN - 2507-7961
pISSN - 0856-1761
DOI - 10.4314/tjs.v47i4.5
Subject(s) - inversion (geology) , mathematics , iterative method , matrix (chemical analysis) , hermitian matrix , matrix splitting , symmetric matrix , nonlinear system , convergence (economics) , integer (computer science) , mathematical analysis , mathematical optimization , state transition matrix , computer science , physics , pure mathematics , paleontology , eigenvalues and eigenvectors , materials science , structural basin , quantum mechanics , economics , composite material , biology , programming language , economic growth
In this paper, we propose the inversion free iterative method to find symmetric solution of thenonlinear matrix equation β β = ( β₯ ), where is an unknown symmetricsolution, is a given Hermitian matrix and is a positive integer. The convergence of theproposed method is derived. Numerical examples demonstrate that the proposed iterative methodis quite efficient and converges well when the initial guess is sufficiently close to the approximatesolution.
Keywords: Symmetric solution, nonlinear matrix equation, inversion free, iterative method