# Approximate Inverse Techniques for Block-Partitioned Matrices

@article{Chow1997ApproximateIT, title={Approximate Inverse Techniques for Block-Partitioned Matrices}, author={Edmond Chow and Yousef Saad}, journal={SIAM J. Sci. Comput.}, year={1997}, volume={18}, pages={1657-1675} }

This paper proposes some preconditioning options when the system matrix is in block-partitioned form. This form may arise naturally, for example, from the incompressible Navier--Stokes equations, or may be imposed after a domain decomposition reordering. Approximate inverse techniques are used to generate sparse approximate solutions whenever these are needed in forming the preconditioner. The storage requirements for these preconditioners may be much less than for incomplete LU factorization…

## 117 Citations

### BLOCK ILU PRECONDITIONED ITERATIVE METHODS FOR REDUCED LINEAR SYSTEMS

- Computer Science, Mathematics

A block red-black coloring technique is introduced to reorder the unknowns, which is based on the standard red- black coloring, for iterative solution of a large sparse matrix when this matrix is in block-partitioned form arising from discrete elliptic Partial Differential Equations (PDEs).

### A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems

- Computer ScienceSIAM J. Sci. Comput.
- 1998

A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient--type methods.

### BLOCK APPROXIMATE INVERSE PRECONDITIONERS FOR SPARSE NONSYMMETRIC LINEAR SYSTEMS

- Computer Science
- 2010

In this paper block approximate inverse preconditioners to solve sparse nonsymmetric linear systems with iterative Krylov subspace methods are studied. The computation of the preconditioners involves…

### Finite-element based sparse approximate inverses for block-factorized preconditioners

- Computer Science, MathematicsAdv. Comput. Math.
- 2011

A method to construct numerically efficient and computationally cheap sparse approximations of some of the matrix blocks arising in the block-factorized preconditioners for matrices with a two-by-two block structure for scalar elliptic problems is analysed.

### INCREMENTAL INCOMPLETE LU FACTORIZATIONS WITH APPLICATIONS TO TIME-DEPENDENT PDES

- Mathematics, Computer Science
- 2008

This papers examines a number of techniques for computing incremental ILU factorizations based on approximate inverses as well as alternating techniques for updating the factors L and U of the factorization.

### Some Preconditioners for Block Pentadiagonal Linear Systems Based on New Approximate Factorization Methods

- Computer Science, Mathematics
- 2013

An high-efficiency parallel algorithm to solve sparse block pentadiagonal linear systems suitable for vectors and parallel processors, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners that are appropriate when the desired target is to maximize parallelism.

### Incremental incomplete LU factorizations with applications

- Computer Science, MathematicsNumer. Linear Algebra Appl.
- 2010

A number of techniques for computing incremental ILU factorizations are examined, including methods based on approximate inverses as well as alternating techniques for updating the factors L and U of the factorization.

### On some new approximate factorization methods for block tridiagonal matrices suitable for vector and parallel processors

- Computer Science, MathematicsMath. Comput. Simul.
- 2009

### The effect of block red-black ordering on blockILU preconditioner for sparse matrices

- Computer Science
- 2005

A block red-black coloring is introduced to increase the degree of parallelism in the application of the blockILU preconditioner for solving sparse matrices, arising from convection-diffusion equations discretized using the finite difference scheme (five-point operator).

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