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The university of Florida sparse matrix collection
Timothy A. Davis, Yifan Hu
Article No.: 1
We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications. The Collection is widely used by the numerical linear algebra community for the development and...
Exploiting parallelism in matrix-computation kernels for symmetric multiprocessor systems: Matrix-multiplication and matrix-addition algorithm optimizations by software pipelining and threads allocation
Paolo D'alberto, Marco Bodrato, Alexandru Nicolau
Article No.: 2
We present a simple and efficient methodology for the development, tuning, and installation of matrix algorithms such as the hybrid Strassen's and Winograd's fast matrix multiply or their combination with the 3M algorithm for complex matrices...
Computing the volume of a union of balls: A certified algorithm
Frederic Cazals, Harshad Kanhere, Sébastien Loriot
Article No.: 3
Balls and spheres are amongst the simplest 3D modeling primitives, and computing the volume of a union of balls is an elementary problem. Although a number of strategies addressing this problem have been investigated in several communities,...
High-performance up-and-downdating via householder-like transformations
Robert A. Van De Geijn, Field G. Van Zee
Article No.: 4
We present high-performance algorithms for up-and-downdating a Cholesky factor or QR factorization. The method uses Householder-like transformations, sometimes called hyperbolic Householder transformations, that are accumulated so that most...
Algorithm 913: An elegant IDR(s) variant that efficiently exploits biorthogonality properties
Martin B. Van Gijzen, Peter Sonneveld
Article No.: 5
The IDR(s) method that is proposed in Sonneveld and van Gijzen  is a very efficient limited memory method for solving large nonsymmetric systems of linear equations. IDR(s) is based on the induced dimension reduction theorem,...
Algorithm 914: Parabolic cylinder function W(a, x) and its derivative
Amparo Gil, Javier Segura, Nico M. Temme
Article No.: 6
A Fortran 90 program for the computation of the real parabolic cylinder functions W(a, ± x), x ≥ 0 and their derivatives is presented. The code also computes scaled functions for a > 50. The...
Remark on “algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization”
José Luis Morales, Jorge Nocedal
Article No.: 7
This remark describes an improvement and a correction to Algorithm 778. It is shown that the performance of the algorithm can be improved significantly by making a relatively simple modification to the subspace minimization phase. The correction...
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
Timothy A. Davis
Article No.: 8
SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across...
Corrigendum: Algorithm 902: GPOPS, a MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method
Anil V. Rao, David A. Benson, Christopher Darby, Michael A. Patterson, Camila Francolin, Ilyssa Sanders, Geoffrey T. Huntington
Article No.: 9
An algorithm is described to solve multiple-phase optimal control problems using a recently developed numerical method called the Gauss pseudospectral method. The algorithm is well suited for use in modern vectorized programming languages...