An interval extension of SMS method for computing weighted Moore–Penrose inverse

Abstract

An interval extension of successive matrix squaring (SMS) method for computing the weighted Moore---Penrose inverse $$A^{\dagger }_{MN}$$AMN? along with its rigorous error bounds is proposed for given full rank $$m \times n$$m?n complex matrices A, where M and N be two Hermitian positive definite matrices of orders m and n, respectively. Starting with a suitably chosen complex interval matrix containing $$A^{\dagger }_{MN}$$AMN?, this method generates a sequence of complex interval matrices each enclosing $$A^{\dagger }_{MN}$$AMN? and converging to it. A new method is developed for constructing initial complex interval matrix containing $$A^{\dagger }_{MN}$$AMN?. Convergence theorems are established. The R-order convergence is shown to be equal to at least l, where $$l \ge 2$$l?2. A number of numerical examples are worked out to demonstrate its efficiency and effectiveness. Graphs are plotted to show variations of the number of iterations and computational times compared to matrix dimensions. It is observed that ISMS is more stable compared to SMS.