Representations and expansions of weighted pseudoinverse matrices, iterative methods, and problem regularization. II. Singular weights

The paper reviews studies on the representations and expansions of weighted pseudoinverse matrices with positive semidefinite weights and on the construction of iterative methods and regularized problems for the calculation of weighted pseudoinverses and weighted normal pseudosolutions based on these representations and expansions. The use of these methods to solve constrained least squares problems is examined. Continued from Cybernetics and Systems Analysis, 44, No. 1, 36–55 (2008). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 75–102, May–June 2008.