Existence and uniqueness of weighted pseudoinverse matrices and weighted normal pseudosolutions with singular weights

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

Abstract

For one of definitions of weighted pseudoinversion with singular weights, necessary and sufficient conditions for the existence and uniqueness are obtained. Expansions of weighted pseudoinverse matrices in matrix power series and matrix power products are obtained. Relationship is established between the weighted pseudoinverse matrices and the weighted normal pseudosolutions. Iterative methods for the calculation of both weighted pseudoinverse matrices and weighted normal pseudosolutions are constructed.
Published
25.01.2011
How to Cite
Galba, E. F., V. S. Deineka, and I. V. Sergienko. “Existence and Uniqueness of Weighted Pseudoinverse Matrices and Weighted Normal Pseudosolutions With Singular Weights”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 1, Jan. 2011, pp. 80-101, https://umj.imath.kiev.ua/index.php/umj/article/view/2700.
Section
Research articles