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**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...