GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Updating the inverse of a matrix
SIAM Review
Matrix computations (3rd ed.)
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Computing entries of the inverse of a sparse matrix using the FIND algorithm
Journal of Computational Physics
Low cost high performance uncertainty quantification
Proceedings of the 2nd Workshop on High Performance Computational Finance
SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.00 |
This paper presents two methods based on domain decomposition concepts for determining the diagonal of the inverse of specific matrices. The first uses a divide-and-conquer principle and the Sherman-Morrison-Woodbury formula and assumes that the matrix can be decomposed into a $2 \times 2$ block-diagonal matrix and a low-rank matrix. The second method is a standard domain decomposition approach in which local solves are combined with a global correction. Both methods can be successfully combined with iterative solvers and sparse approximation techniques. The efficiency of the methods usually depends on the specific implementation, which should be fine-tuned for different test problems. Preliminary results for some two-dimensional (2D) problems are reported to illustrate the proposed methods.