GSoC Part 2

Now follows the second part of the Google Summer of Code. Here is what I planned to do in that time.

Goals for the Final Evaluation 2013-09-16 (Monday, "Suggested 'pencils down' date") :

• Implementations for IC(0) and ICT completed
• Wrapper file for MATLAB compatibility (ichol.m) finished
• Small test cases for all incomplete-factorizations
• Documentation of incomplete LU-factorization types
• Comprehensive test cases for all types of incomplete-factorization types (also  proofing compatibility to MATLAB)
• (optional) Complex version for the incomplete-factorizations

TODOs:

• Clean the development repository.
• Upload the changes
• Discuss and decide for implementation of IC(0) and ICT
• Paper [Jones_Plassmann_1991] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.5862 and a Fortran implementation from the ACM [Jones_Plassmann_1995] http://doi.acm.org/10.1145/200979.200986
• Already requested the authors for free usage
• Via an Paper [Munksgaard_1980] https://dl.acm.org/citation.cfm?doid=355887.355893 I got attention to the HSL (formerly the Harwell Subroutine Library) http://www.hsl.rl.ac.uk/ which also has a Fortran implementation of ICs. Problem the license again.
• Already requested the authors for free usage
• Paper [Benzi_2002] http://www.mathcs.emory.edu/~benzi/Web_papers/survey.pdf describes really all-encompassing preconditioning. Michele Benzi and Miroslav Tůma still have the sources for their survey including some MATLAB interface. http://www2.cs.cas.cz/~tuma/sparslab.html
• Free Software
• Paper [Lin_MORÉ_1999] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.1636 present a MATLAB pseudocode based upon [Jones_Plassmann_1995]. No straight forward implementation possible.
• Saad gives small pseudocodes in a paper [Saad_1992] http://www-users.cs.umn.edu/~saad/PDF/RIACS-ILQ-TR.pdf and in his book [Saad_2003] http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf about the IC(0). The Mathworks cites Saad's book and a paper [Manteuffel_1980] http://www.ams.org/journals/mcom/1980-34-150/S0025-5718-1980-0559197-0/S0025-5718-1980-0559197-0.pdf which describes the shifting algorithm mathematically.