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, a new efficient computational algorithm is presented for solving cyclic heptadiagonal linear systems based on using of heptadiagonal linear solver and Sherman–Morrison–Woodbury formula. The implementation of the algorithm using computer algebra systems (CAS) such as MAPLE and MATLAB is straightforward. Numerical example is presented for the sake of illustration.

We present some results on generalized inverses and their application to generalizations of the Sherman-Morrison-Woodbury-type formulae.

We discuss the use of a matrix-oriented approach for numerically solving dense matrix equation AX + XAT M1XN1 … MℓXNℓ = F, with ℓ ≥ 1, and Mi, Ni, i , low rank. The relies on Sherman–Morrison–Woodbury formula formally defined in vectorized form problem, but applied setting. This allows one to solve medium size problems computational costs memory requirements dramatically lower than Kronecker fo...

Our motivation is to derive the Drazin inverse matrix modification formulae utilizing inverses of adequate Peirce corners under some special cases, and a with an additive perturbation. As applications, several new results for expressions modified matrices A ?? CB CDdB are obtained, well known in literature, as Sherman-Morrison-Woodbury formula Jacobson?s Lemma, generalized.

This paper describes an algorithm to improve a computational cost for estimation using the Kriging method with a large number of sampling data. An improved formula to compute the weighting coefficient for Kriging estimation is proposed. The Sherman–Morrison–Woodbury formula is applied to solving an approximated simultaneous equation to determine a weighting coefficient. A profile of the matrix ...

According to our previous theoretical and experimental study, additive preconditioners can be readily computed for ill conditioned matrices, but application of such preconditioners to facilitating matrix computations, in particular to solving linear systems of equations, is not straightforward. In the present paper we develop some nontrivial techniques for the latter task. By applying the Sherm...