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Digital filters in adaptive time-stepping
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
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
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
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
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...