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

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

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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
• Improve given factorized preconditioners such as ILU, AINV, FSAI, FSPAI, etc subject to probing subspaces
• Compute sparse spectrally equivalent approximations to dense or even full matrices

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
• Full support for complex problems in all features

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

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