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Convergence of Rump's method for computing the Moore-Penrose inverse

Yunkun Chen; Xinghua Shi; Yi Min Wei — 2016

Czechoslovak Mathematical Journal

We extend Rump's verified method (S. Oishi, K. Tanabe, T. Ogita, S. M. Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices with full column (row) rank. We establish the convergence of our numerical verified method for computing the Moore-Penrose inverse. We also discuss the rank-deficient case and test some ill-conditioned examples. We provide our Matlab codes for computing the...

Integral representations of the $g$ -Drazin inverse in $C^{*}$ -algebras

N. Castro González; Jaromír J. Koliha; Yi Min Wei — 2004

Mathematica Bohemica

The paper gives new integral representations of the $g$ -Drazin inverse of an element $a$ of a $C^{*}$ -algebra that require no restriction on the spectrum of $a$ . The representations involve powers of $a$ and of its adjoint.

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Convergence of Rump's method for computing the Moore-Penrose inverse

Integral representations of the g -Drazin inverse in C * -algebras

Integral representations of the $g$ -Drazin inverse in $C^{*}$ -algebras