#### 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...