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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.

international journal of computer mathematics

On an inversion-free algorithm for the nonlinear matrix problem                                                                                                    X                                                                                  α                                                                         +                                                                               A                                                                                  ∗                                                                                                                                X                                                                                  −                              β                                                                                                   A                                               +                                                                               B                                                                                  ∗                                                                                                                                X                                                                                  −                              γ                                                                                                   B                                               =                                                  I                                               ,