On an inversion-free algorithm for the nonlinear matrix problem Xα+A∗X−βA+B∗X−γB=I,
Sourav Shil, Hemant Kumar Nashine, Fazlollah Soleymani
Abstract
We perform extensive theoretical analysis on an inversion-free algorithm to obtain a maximal positive definite solution (PDS) of a general nonlinear matrix equation (NME) with suitable square matrices. We illustrate some estimations for obtaining the solution, rate of convergence and convergence analysis of the presented algorithm. To ensure its validity and usefulness, several different types of test problems, including randomly generated ones, are given. Comparisons with the existing iterative methods are done through error and computational time.
Topics & Concepts
MathematicsInversion (geology)AlgorithmRate of convergenceConvergence (economics)Nonlinear systemIterative methodMatrix (chemical analysis)Applied mathematicsPositive-definite matrixComputer scienceEigenvalues and eigenvectorsQuantum mechanicsEconomic growthEconomicsMaterials scienceBiologyComputer networkStructural basinComposite materialPhysicsPaleontologyChannel (broadcasting)Matrix Theory and AlgorithmsIterative Methods for Nonlinear EquationsAdvanced Optimization Algorithms Research