Weighted pseudoinversion with indefinite weights - Vareniuk, N. A.; Galba, E. F.; Sergienko, I. V.; Khimich, A. N. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
We present the definition of weighted pseudoinverse matrices with nonsingular indefinite weights and study these matrices.The theorems on existence and uniqueness for these matrices are proved. Weighted pseudoinverse matrices withindefinite weights are represented in terms of the coefficients of characteristic polynomials of symmetrizable matrices.The decompositions of weighted pseudoinverse matrices into matrix power series and products and their limit representationsare obtained. We also propose regularized iterative methods for the determination of these matrices.