Fast convergent iterative methods for the computation of weighted pseudoinverses and weighted normal pseudosolutions with singular weights

To calculate weighted pseudoinverses and weighted normal pseudosolutions with singular weights, iterative processes with the convergence order $p\ge 2$ are constructed and analyzed. Expansions of weighted pseudoinverses in matrix power products are obtained and used in the construction of those processes. The issue of the adaptation of the iterative processes designed for the computation of weighted normal pseudosolutions to solving constrained least squares problems is examined.