According to our previous theoretical and experimental study, additive preconditioners can be readily computed for ill conditioned matrices, but it is not straightforward how such preconditioners can help us to facilitate the solution of linear systems of equations, computation of determinants, and other fundamental matrix computations. We develop some nontrivial techniques for this task. By ap...

According to our previous theoretical and experimental study, additive preconditioners can be readily computed for ill conditioned matrices, but it is not straightforward how such preconditioners can help us to facilitate the solution of linear systems of equations, computation of determinants, and other fundamental matrix computations. We develop some nontrivial techniques for this task. By ap...

We present several methods for the efficient implementation of the Ensemble Kalman Filter (EnKF) of Evensen. It is shown that the EnKF can be implemented without access to the observation matrix, and only an observation function is needed; this greatly simplifies software design. New implementations of the EnKF formulas are proposed, with linear computational complexity in the number of data po...

According to our previous theoretical and experimental study, additive preconditioners can be readily computed for ill conditioned matrices, but it is not straightforward how such preconditioners can help us to facilitate the solution of linear systems of equations, computation of determinants, and other fundamental matrix computations. We develop some nontrivial techniques for this task. By ap...

Abstract Models in which the covariance matrix has structure of a sparse plus low rank perturbation are ubiquitous data science applications. It is often desirable for algorithms to take advantage such structures, avoiding costly computations that require cubic time and quadratic storage. This accomplished by performing operations maintain example, inversion via Sherman–Morrison–Woodbury formul...

A matrix inversion algorithm based on the Sherman-Morrison formula is analyzed and compared with the classical Gauss-Jordan algorithm. In particular the results obtained in a Cray T3-E by the parallel versions of both algorithms are compared. Key-Words:Sherman-Morrison formula, matrix inversion, Parallel algorithms, Cray T3-E

We focus on the group inverse of modified matrices M = A−BC, where A is an n×n matrix with entries in an arbitrary ring R with unity and B, n×k, and C, k×n, are matrices having entries in R. We assume that A has the group inverse and we give conditions that guarantee the existence of the group inverse of M . We present an extension of the Sherman-Morrison-Woodbury formulae for the group inverse...

We focus on the group inverse of modified matrices M = A−BC, where A is an n×n matrix with entries in an arbitrary ring R with unity and B, n×k, and C, k×n, are matrices having entries in R. We assume that A has the group inverse and we give conditions that guarantee the existence of the group inverse of M . We present an extension of the Sherman-Morrison-Woodbury formulae for the group inverse...