Remarks on the Sherman-morrison-woodbury Formulae
ثبت نشده
چکیده
We present some results on generalized inverses and their application to generalizations of the Sherman-Morrison-Woodbury-type formulae.
منابع مشابه
Some Modifications to Calculate Regression Coefficients in Multiple Linear Regression
In a multiple linear regression model, there are instances where one has to update the regression parameters. In such models as new data become available, by adding one row to the design matrix, the least-squares estimates for the parameters must be updated to reflect the impact of the new data. We will modify two existing methods of calculating regression coefficients in multiple linear regres...
متن کاملA generalization of the Sherman-Morrison-Woodbury formula
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.
متن کاملEla Group Inverse of Modified Matrices over an Arbitrary Ring
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...
متن کاملGroup inverse of modified matrices over an arbitrary ring
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...
متن کاملA New Algorithm for General Cyclic Heptadiagonal Linear Systems Using Sherman-Morrison-Woodbury formula
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.
متن کامل