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ACM Transactions on Mathematical Software (TOMS), Volume 34 Issue 3, May 2008

Anatomy of high-performance matrix multiplication
Kazushige Goto, Robert A. van de Geijn
Article No.: 12
DOI: 10.1145/1356052.1356053

We present the basic principles that underlie the high-performance implementation of the matrix-matrix multiplication that is part of the widely used GotoBLAS library. Design decisions are justified by successively refining a model of...

An event-driven method to simulate Filippov systems with accurate computing of sliding motions
Petri T. Piiroinen, Yuri A. Kuznetsov
Article No.: 13
DOI: 10.1145/1356052.1356054

This article describes how to use smooth solvers for simulation of a class of piecewise smooth systems of ordinary differential equations, called Filippov systems, with discontinuous vector fields. In these systems constrained motion along a...

Cache efficient bidiagonalization using BLAS 2.5 operators
Gary W. Howell, James W. Demmel, Charles T. Fulton, Sven Hammarling, Karen Marmol
Article No.: 14
DOI: 10.1145/1356052.1356055

On cache based computer architectures using current standard algorithms, Householder bidiagonalization requires a significant portion of the execution time for computing matrix singular values and vectors. In this paper we reorganize the sequence...

Algorithm 874: BACOLR—spatial and temporal error control software for PDEs based on high-order adaptive collocation
R. Wang, P. Keast, P. H. Muir
Article No.: 15
DOI: 10.1145/1356052.1356056

In this article we discuss a new software package, BACOLR, for the numerical solution of a general class of time-dependent 1-D PDEs. This package employs high-order adaptive methods in time and space within a method-of-lines approach and provides...

Algorithm 875: DSDP5—software for semidefinite programming
Steven J. Benson, Yinyu Ye
Article No.: 16
DOI: 10.1145/1356052.1356057

DSDP implements the dual-scaling algorithm for semidefinite programming. The source code for this interior-point algorithm, written entirely in ANSI C, is freely available under an open source license. The solver can be used as a subroutine...