MSPAI

Modified Sparse Approximate Inverses

This is a dummy textCurrent version is 1.1

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-1.1.tar.gz.
• MSPAI manual, closely adapted from SPAI 3.2 manual: mspai-1.1.pdf.

• HTML documentation of source code: html-mspai-1.1.tar.gz.
• Source code and HTML documentation: mspai-1.1-html.tar.gz.

Thesis on MSPAI

• 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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