In this paper, we develop conditions under which the Sherman–Morrison–Woodbury formula can be represented in the Moore–Penrose inverse and the generalized Drazin inverse forms. These results generalize the original Sherman–Morrison–Woodbury formula. © 2011 Elsevier Ltd. All rights reserved.

We study the eigenvalue problem for a specially structured rank-k updated matrix, based on the Sherman–Morrison– Woodbury formula. 2006 Elsevier Inc. All rights reserved.

In this paper, we investigate the Sherman-Morrison-Woodbury formula for {1}-inverses and {2}-inverses of bounded linear operators on a Hilbert space. Some conditions are established to guarantee that (A+YGZ*)? = A? ?A?Y(G? +Z*A?Y)?Z*A? holds, where stands any kind standard inverse, {1}-inverse, {2}-inverse, Moore-Penrose Drazin group core inverse dual A.

In this paper, based on the structure of pentadiagonal CUPL-Toeplitz matrix and Sherman–Morrison–Woodbury formula, we develop a new algorithm for solving nonsingular linear system. Some numerical examples are given in order to illustrate effectiveness proposed algorithms.

We apply our recent preconditioning techniques to the solution of linear systems of equations and computing determinants. We combine these techniques with the Sherman–Morrison–Woodbury formula, its new variations, aggregation, iterative refinement, and advanced algorithms that rapidly compute sums and products either error-free or with the desired high accuracy. Our theoretical and experimental...

In this paper, we propose a continuous time model for modeling the spread of HIV in a network of prisons. We give some sufficient conditions for the equilibrium points of the system to be stable. We also develop an efficient algorithm based on Newton’s method and the Sherman-Morrison-Woodbury Formula for computing the equilibrium values of the infectives in each prison.

This paper establishes some perturbation analysis for the tensor inverse, Moore-Penrose and system based on t-product. In settings of structured perturbations, we generalize Sherman-Morrison-Woodbury (SMW) formula to t-product scenarios. The SMW can be used perform sensitivity a multilinear equations.