An interval extension of SMS method for computing weighted Moore-Penrose inverse (Q723553)

The paper is concerned with the Successive Matrix Squaring (SMS) algorithm for computing the weighted Moore-Penrose inverse \(A^{+}_{M N}\). For full rank \(m \times n\) matrices \(A\), and Hermitian positive definite \(M\) and \(N\) the authors construct an interval arithmetic extension of the SMS iteration. This extension generates a sequence of complex interval matrices, each of them containing \(A^{+}_{M N}\). The authors prove convergence of the new method and show by numerical experiments its better stability compared with the classical SMS algorithm.