Displaying similar documents to “Positive splittings of matrices and their nonnegative Moore-Penrose inverses”

Some equalities for generalized inverses of matrix sums and block circulant matrices

Yong Ge Tian (2001)

Archivum Mathematicum

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Let A 1 , A 2 , ⋯ , A n be complex matrices of the same size. We show in this note that the Moore-Penrose inverse, the Drazin inverse and the weighted Moore-Penrose inverse of the sum ∑ t = 1 n A t can all be determined by the block circulant matrix generated by A 1 , A 2 , ⋯ , A n . In addition, some equalities are also presented for the Moore-Penrose inverse and the Drazin inverse of a quaternionic matrix.

On the generalized Drazin inverse and generalized resolvent

Dragan S. Djordjević, Stanimirović, Predrag S. (2001)

Czechoslovak Mathematical Journal

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We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in C * -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range...

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

Yunkun Chen, Xinghua Shi, Yi Min Wei (2016)

Czechoslovak Mathematical Journal

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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...