On a Method for Computing Pseudoinverses

Abstract

Let A be a continuous linear operator with domain of definition D(A)=X and range of values R(A)=Y, where Xand Y are Hilbert spaces. We are given an element yεY and a subset M⊂X,and the problem of finding an element xεM which solves the equation

$$\text{Ax}\,\text{=}\,\text{y}\,\text{,y }\!\!\varepsilon\!\!\text{ Y}\,\text{,x }\!\!\varepsilon\!\!\text{ M}\subset \text{X}$$

(1)