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.
• 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): pdf.
• Further details about implementation (german only): pdf.

MSPAI References

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• For further references on Sparse Approximate Inverses see this page.

Authors

• Thomas Huckle
• Alexander Kallischko
• Matous Sedlacek

License

MSPAI: Modified Sparse Approximate Inverses
Copyright © 2007, 2008, Thomas Huckle, Alexander Kallischko and Matous Sedlacek.

This program is free software: you can redistribute it and/or modify it under the
terms of the GNU Lesser General Public License as published by the Free Software
Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with
this program. If not, see http://www.gnu.org/licenses/.

If you obtain any results with MSPAI we would appreciate that you refer to MSPAI.

Funding

This work has partially been funded by Bund der Freunde der Technischen Universität München e.V. (BdF),
Antrag 2008-09.