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[http://hg.savannah.gnu.org/hgweb/octave/file/119ce9f5e1a3/scripts/sparse/gmres.m gmres] or [http://hg.savannah.gnu.org/hgweb/octave/file/119ce9f5e1a3/scripts/sparse/pcg.m pcg].
The classic book [http://netlib.org/linalg/html_templates/node81.html Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods] has a [http://netlib.org/linalg/html_templates/node100.html#SECTION00933000000000000000 chapter] describing the
ILU algorithm in detail, though the algorithm described there should be adapted to Octave's internal Sparse Matrix file format which is [http://netlib.org/linalg/html_templates/node92.html#SECTION00931200000000000000 CCS] rather than [http://netlib.org/linalg/html_templates/node91.html#SECTION00931100000000000000 CRS]. The implementation of ILU in Octave has been recently discussed in the maintainers list and initial implementations were posted in this [http://octave.1599824.n4.nabble.com/Ilu-function-tp4648677.html thread]. In another [http://octave.1599824.n4.nabble.com/Re-Octave-maintainers-Digest-Vol-80-Issue-15-tp4646303.html thread] it was suggested to implement the ILU by interfacing Octave to [http://www-users.cs.umn.edu/~saad/software/ITSOL/ ITSOL] . Compared to other projects in this section this one might require more knowledge of C++.
=== Improve logm, sqrtm, funm ===
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