The computation of some entries of a matrix inverse arises in several important applications in practice. This paper presents a probing method for determining the diagonal of the inverse of a sparse matrix in the common situation when its inverse exhibits a decay property. A few simple properties of the inverse suggest a way to determine effective probing vectors based on standard graph theory results. An iterative method is then applied to solve the resulting sequence of linear systems, from which the diagonal of the matrix inverse is extracted. Results of numerical experiments are provided to demonstrate the effectiveness of the proposed method.
|Original language||English (US)|
|Number of pages||4|
|Journal||HKIE Transactions Hong Kong Institution of Engineers|
|State||Published - 2010|
Bibliographical noteFunding Information:
Work supported in part by DOE under grant DE-FG 08ER 25841, by NSF under grant OCI-0904587, and by the Minnesota Supercomputer Institute. The authors are indebted to Mr Chen Jie for providing the covariance matrix generator, Mr Fang Hawren for his comments on this paper, and Mr Pierre Carrier for his help with the DMFT code.
- Covariance Matrices
- Graph Theory
- Green’s Functions
- Krylov-subspace Methods
- Matrix Diagonal Extraction
- Sparse Approximate Inverses