MSPAI

Modified Sparse Approximate Inverses -- UNDER CONSTRUCTION!!!

Based upon the well-known sparse approximate inverse preconditioner SPAI, we developed the modified sparse approximate inverse (MSPAI) preconditioner.

Theory

MSPAI is a preconditioner for large sparse and ill-conditioned systems of linear equations. We extended the basic SPAI minimization

Error creating thumbnail: Unable to save thumbnail to destination

to target form and further generalized it in order to add additional probing constraints:

Error creating thumbnail: Unable to save thumbnail to destination

For an overview of the versatile employment possibilities of our MSPAI formulation, see this pdf taken from here.

Implementation and Features

The entire implementation is done in C++ with parallelization in MPI. Except the Block SPAI approach, we cover the full functionality of SPAI 3.2.

Methodical improvements

• Extension to target form: allow probing
• Support for explicit and inverse approximations, both in factorized and unfactorized form and probing of Schur complements, see pdf

Technical improvements

• Support for complex valued problems
• Support for sparse QR methods using CSparse by Tim Davis
• Caching approach to avoid redundant QR decompositions
• Implementation of QR updates to accelerate pattern update steps
• Support for maximum sparsity patterns
• Arbitrary start patterns, i.e. possibility to compute a static SPAI without pattern update steps

Todo

• Mex interface for MATLAB
• PetSc interface
• Support for other LAPACK implementations than ATLAS
• Wider coverage of file formats for sparse matrices, now support for Matrix Market format only

Download

• MSPAI 1.1 source code tar ball: []
• MSPAI manual, closely adapted from SPAI 3.2 manual: []

• Ph.D. thesis about MSPAI, both theory and implementation: mediatum
• Details about sparse QR methods in SPAI applications (german only): []
• Further details about implementation (german only): pdf

MSPAI References

<pubsccs>nocaption=1&persid=53&utypid=1020&datum=2007&lang=en</pubsccs><pubsccs>nocaption=1&persid=53&utypid=2030&datum=2008&lang=en</pubsccs>

under construction -- more information about MSPAI implementation and download will be available soon.