Expansion of weighted pseudoinverse matrices with singular weights into matrix power products and iteration methods

  • E. F. Galba
  • V. S. Deineka
  • I. V. Sergienko

Abstract

We obtain expansions of weighted pseudoinverse matrices with singular weights into matrix power products with negative exponents and arbitrary positive parameters. We show that the rate of convergence of these expansions depends on a parameter. On the basis of the proposed expansions, we construct and investigate iteration methods with quadratic rate of convergence for the calculation of weighted pseudoinverse matrices and weighted normal pseudosolutions. Iteration methods for the calculation of weighted normal pseudosolutions are adapted to the solution of least-squares problems with constraints.
Published
25.09.2007
How to Cite
GalbaE. F., DeinekaV. S., and SergienkoI. V. “Expansion of Weighted Pseudoinverse Matrices With Singular Weights into Matrix Power Products and Iteration Methods”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 9, Sept. 2007, pp. 1269–1289, https://umj.imath.kiev.ua/index.php/umj/article/view/3387.
Section
Research articles