I'd like to announce a new book in the SIAM Series on the Fundamental of
Algorithms (
http://www.siam.org/books/series/fundalgo.php),
entitled "Direct Methods for Sparse Linear Systems." The goal of the
book is to illustrate the theory and practice of direct methods for
solving sparse linear systems. Towards that end, a new package was
written for the book: CSparse, a Concise Sparse matrix package. Its
2200 lines of C are printed in their entirety in the book, and available
for download at
http://www.cise.ufl.edu/research/sparse/CSparse. A
MATLAB interface is provided.
Topics in the book (and methods in CSparse) include basic algorithms and
data structures (triplet form, compressed column form, add, multiply,
transpose, permute, norms), solving triangular systems with both dense
and sparse right-hand sides, Cholesky, LU and QR factorizations,
Cholesky update/downdate, ordering methods (minimum degree and dmperm;
profile orderings and nested dissection are done as short m-files), and
finally culminating in x=A\b. The book also describes how MATLAB
performs its sparse matrix computations.
Today (Sept 15) is the target date for publication, so it should
either be available now, or in just a few days.
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