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ACM Transactions on Mathematical Software (TOMS), Volume 29 Issue 1, March 2003

Digital filters in adaptive time-stepping
Gustaf Söderlind
Pages: 1-26
DOI: 10.1145/641876.641877
Adaptive time-stepping based on linear digital control theory has several advantages: the algorithms can be analyzed in terms of stability and adaptivity, and they can be designed to produce smoother stepsize sequences resulting in significantly...

Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit
Yves Nievergelt
Pages: 27-48
DOI: 10.1145/641876.641878
Combined with doubly compensated summation, scalar fused multiply-add instructions redefine the concept of floating-point arithmetic, because they allow for the computation of sums of real or complex matrix products accurate to the penultimate digit....

Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator
Stephen Joe, Frances Y. Kuo
Pages: 49-57
DOI: 10.1145/641876.641879
An algorithm to generate Sobol' sequences to approximate integrals in up to 40 dimensions has been previously given by Bratley and Fox in Algorithm 659. Here, we provide more primitive polynomials and "direction numbers" so as to allow the generation...

Object-oriented software for quadratic programming
E. Michael Gertz, Stephen J. Wright
Pages: 58-81
DOI: 10.1145/641876.641880
The object-oriented software package OOQP for solving convex quadratic programming problems (QP) is described. The primal-dual interior point algorithms supplied by OOQP are implemented in a way that is largely independent of the problem structure....

Induced well-distributed sets in Riemannian spaces
Lothar Wenzel, Ram Rajagopal, Dinesh Nair
Pages: 82-94
DOI: 10.1145/641876.641881
The concept of Riemannian geometries is used to construct induced homogeneous point sets on manifolds that are based on well-distributed point sets in unit cubes of an appropriately chosen Euclidean space. These well-distributed point sets in unit...