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ACM Transactions on Mathematical Software (TOMS), Volume 24 Issue 2, June 1998

An object-oriented framework for block preconditioning
Edmond Chow, Michael A. Heroux
Pages: 159-183
DOI: 10.1145/290200.287639
General software for preconditioning the iterative solution of linear systems is greatly lagging behind the literature. This is partly because specific problems and specific matrix and preconditioner data structures in order to be solved...

Algorithm 781: generating Hilbert's space-filling curve by recursion
Greg Breinholt, Christoph Schierz
Pages: 184-189
DOI: 10.1145/290200.290219
An efficient algorithm for the generation of Hilbert's space-filling curve is given. The algorithm implements a recursive procedure that involves simple integer operations and quickly converges to the set of points that make the Hilbert curve....

The automatic generation of sparse primitives
Aart J. C. Bik, Peter J. H. Brinkhaus, Peter M. W. Knijnenburg, Harry A. G. Wijshoff
Pages: 190-225
DOI: 10.1145/290200.287636
Primitives in mathematical software are usually written and optimized by hand. With the implementation of a “sparse compiler” that is capable of automatically converting a dense program into sparse code, however, a completely...

Computing rank-revealing QR factorizations of dense matrices
Christian H. Bischof, G. Quintana-Ortí
Pages: 226-253
DOI: 10.1145/290200.287637
We develop algorithms and implementations for computing rank-revealing QR (RRQR) factorizations of dense matrices. First, we develop an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the...

Algorithm 782: codes for rank-revealing QR factorizations of dense matrices
C. H. Bischof, G. Quintana-Ortí
Pages: 254-257
DOI: 10.1145/290200.287638
This article describes a suite of codes as well as associated testing and timing drivers for computing rank-revealing QR (RRQR) factorizations of dense matrices. The main contribution is an efficient block algorithm for approximating an RRQR...