Sherman–Morrison–Woodbury formulaIn this paper, we focus on the Moore–Penrose metric generalized inverse of the modified operator B=A+UGV, where A,U,G,V are bounded linear operators between some Banach spaces. We establish conditions that guarantee the existence of the Moore–Penrose metric ...
As a consequence, we present an extension of the so-called classical Sherman–Morrison–Woodbury formula for the Moore–Penrose metric generalized inverse. Some particular cases and applications will be also considered.关键词: Metric generalized inverse perturbation Sherman–Morrison–Woodbury formula ...
To see one reason why this formula is useful, suppose that the matrix and its perturbation are symmetric and we wish to preserve symmetry in our formulas. The Sherman–Morrison–Woodbury requires us to write the perturbation as , so the perturbation must be positive semidefinite. In , however,...
Our approach involves imbedding the surface smoothing problem specified on an irregular domain (in the sense of discontinuities and boundaries) in a rectangular region using the capacitance-matrix method based on the Sherman-Morrison-Woodbury formula of matrix analysis. This formula is used in ...
We note that the Sherman–Morrison formula and the corresponding generalization given by the Sherman–Morrison–Woodbury formula have been used in several applications, such as the solution of special linear systems [11,20,18,29,19,8,9], the solution of linear systems arising in mathematical ...
inverse preconditionerIncomplete factorizationSherman–Morrison–Woodbury formulaa b s t r a c tIn order to solve the Toeplitz-plus-diagonal linear systems arising from image restorationsefficiently, we propose a sparse approximate inverse preconditioner based on theSherman–Morrison–Woodbury formula. The...
Sherman–Morrison–Woodbury formulaSylvester equationWe discuss the use of a matrix﹐riented approach for numerically solving the dense matrix equation AX + XAT + M1XN1 + … + MXN = F, with ≥ 1, and Mi, Ni, i = 1, … , of low rank. The approach relies on the Sherman–Morrison–...
As a consequence, we present an extension of the so-called classical Sherman-Morrison-Woodbury formula for the Moore-Penrose metric generalized inverse. Some particular cases and applications will be also considered.Shi, DongweiHenan Inst Sci & TechnolCao, Jianbing...
Using the Sherman-Morrison-Woodbury Formula to Solve the System of Linear Equations from the Standard Multiple Shooting Method for a Linear Two Point Boundary-Value Problem is a Bad IdeaIvo Hedtke
Our idea is to first solve a bidiagonal system related to the original system of linear equations, and then update it with the Sherman-Morrison-Woodbury formula. We study the feasibility, the numerical stability and the running time of this method. The results are: The method described above ...