Iterative methods with different rates of convergence for calculating weighted pseudoinverse matrices and weighted normal pseudosolutions with positive definite weights

The authors develop and analyze iterative methods with different (linear, quadratic, or of p (p2) order) rates of convergence. The methods are used to calculate weighted pseudoinverse matrices with positive defined weights. To find weighted normal pseudosolutions with positive defined weights, iterative methods with a quadratic rate of convergence are developed and analyzed. The iterative methods for calculation of weighted normal pseudosolutions are used to solve least-square problems with constraints.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 20–44, September–October 2004.