Error bounds in the computation of outer inverses with generalized Schultz iterative methods and its use in computing of Moore-Penrose inverse

Abstract

An error bound in computing of outer inverses is established in each iteration of the generalized Schultz iterative methods. With this error bound, we built class of iterative method for the calculation of the Moore-Penrose inverse, the class of methods uses these error bounds to generate monotonic inclusion interval matrices which congerges to Moore-Penrose inverse, this process using intervals prevents that round-off errors cause the divergence of the method. Theorems with the error bounds as well as the convergence of the new iterative scheme are proved. Numerical examples are presented to demonstrate the efficacy of the new class of methods.