The representation and approximation for the weighted Minkowski inverse in Minkowski space

Abstract

This paper extends some results for the weighted Moore–Penrose inverse A M , N + in Hilbert space to the so-called weighted Minkowski inverse A M , N ⊕ of an arbitrary rectangular matrix A ∈ M m , n in Minkowski spaces μ . Four methods are also used for approximating the weighted Minkowski Inverse A M , N ⊕ . These methods are: Borel summable, Euler–Knopp summable, Newton–Raphson and Tikhonov’s methods.