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Algorithm 933: reliable calculation of numerical rank, null space bases, pseudoinverse solutions, and basic solutions using SuiteSparseQR
Foster L., Davis T. ACM Transactions on Mathematical Software 40(1): 123, 2013. Type: Article
The rank is one of the major characteristics of a matrix. In practice, the rank is not clear cut due to measurement errors and/or noise. Thus, determining the numerical rank of a matrix is an important problem. Many applications require numerical ...
Jan 6 2014
On Ziv’s rounding test
de Dinechin F., Lauter C., Muller J., Torres S. ACM Transactions on Mathematical Software 39(4): 119, 2013. Type: Article
When working in classical finite precision arithmetic, one is often faced with the following problem: the result of a computation cannot be represented exactly. In such cases, one usually has the goal of constructing the computation algorithm so...
Sep 11 2013
Accelerating linear system solutions using randomization techniques
Baboulin M., Dongarra J., Herrmann J., Tomov S. ACM Transactions on Mathematical Software 39(2): 113, 2013. Type: Article
After almost 40 years of active research on parallel scientific computing, researchers are still struggling with the implementation of Gaussian elimination. The problem centers on how to implement pivoting, that is, row and/or column exchanges...
Aug 16 2013
Algorithm 928: a general, parallel implementation of DantzigWolfe decomposition
Rios J. ACM Transactions on Mathematical Software 39(3): 110, 2013. Type: Article
An opensource implementation of the DantzigWolfe decomposition method, a powerful and useful technique for solving linear programming problems of blockangular form, is described in this concise and wellwritten paper....
Jul 5 2013
Variants of Mersenne twister suitable for graphic processors
Saito M., Matsumoto M. ACM Transactions on Mathematical Software 39(2): 120, 2013. Type: Article
Generating sequences of pseudorandom numbers is a prerequisite for many applications, such as Monte Carlo simulations. Since such applications are often executed on parallel computers, the parallel computation of pseudorandom numbers is also...
Jun 5 2013
Graphbased software design for managing complexity and enabling concurrency in multiphysics PDE software
Notz P., Pawlowski R., Sutherland J. ACM Transactions on Mathematical Software 39(1): 121, 2012. Type: Article
The field of complex computational modeling involves the use of advanced hardware and software environments, and the issues faced in the combination of these areas are quite daunting. This paper provides a detailed study of developing software...
May 9 2013
Level3 Cholesky factorization routines improve performance of many Cholesky algorithms
Gustavson F., Wa
niewski J., Dongarra J., Herrero J., Langou J. ACM Transactions on Mathematical Software 39(2): 110, 2013. Type: Article
The Cholesky decomposition of a positive definite matrix is the basis for many efficient and numerically accurate algorithms. The usual procedure is a variant of Gaussian elimination without pivoting, but the computation can be reordered in a...
May 6 2013
Families of algorithms for reducing a matrix to condensed form
Van Zee F., van de Geijn R., QuintanaOrtí G., Elizondo G. ACM Transactions on Mathematical Software 39(1): 132, 2012. Type: Article
As hardware continues to change, developers look for ways to maintain compatibility with current platforms. Right now, the principal issue is that memory bandwidth has not kept up with other changes in hardware, which constrains the performance...
Feb 22 2013
Algorithm 923: efficient numerical computation of the Pfaffian for dense and banded skewsymmetric matrices
Wimmer M. ACM Transactions on Mathematical Software 38(4): 117, 2012. Type: Article
The Pfaffian of a matrix, like the determinant, is a polynomial in the matrix elements. It is most frequently used in particle physics where the matrix is evenordered and skewsymmetric, and the determinant is the square of the Pfaffian. In...
Oct 30 2012
Highperformance upanddowndating via Householderlike transformations
Van De Geijn R., Van Zee F. ACM Transactions on Mathematical Software 38(1): 117, 2011. Type: Article
The linear leastsquares problem in statistics is usually solved by finding the Cholesky factor of the matrix of normal equations. In certain applications, one wants to solve several related problems formed by removing and/or adding data. In this ...
Apr 30 2012
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