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**The university of Florida sparse matrix collection**

Timothy A. Davis, Yifan Hu

Article No.: 1

DOI: 10.1145/2049662.2049663

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

DOI: 10.1145/2049662.2049664

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

DOI: 10.1145/2049662.2049665

Balls and spheres are amongst the simplest 3*D* 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

DOI: 10.1145/2049662.2049666

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

DOI: 10.1145/2049662.2049667

The IDR(*s*) method that is proposed in Sonneveld and van Gijzen [2008] 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

DOI: 10.1145/2049662.2049668

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

DOI: 10.1145/2049662.2049669

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

DOI: 10.1145/2049662.2049670

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

DOI: 10.1145/2049662.2049671

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...