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ACM Transactions on Mathematical Software
1-10 of 346 reviews
Graph-based 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): 1-21, 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
Level-3 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): 1-10, 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., Quintana-Ortí G., Elizondo G. ACM Transactions on Mathematical Software 39(1): 1-32, 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 skew-symmetric matrices
Wimmer M. ACM Transactions on Mathematical Software 38(4): 1-17, 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 even-ordered and skew-symmetric, and the determinant is the square of the Pfaffian. In...
Oct 30 2012
High-performance up-and-downdating via Householder-like transformations
Van De Geijn R., Van Zee F. ACM Transactions on Mathematical Software 38(1): 1-17, 2011. Type: Article
The linear least-squares 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
Algorithm 915, SuiteSparseQR: multifrontal multithreaded rank-revealing sparse QR factorization
Davis T. ACM Transactions on Mathematical Software 38(1): 1-22, 2011. Type: Article
In the area of computational linear algebra, an important topic is the solution of sparse matrix problems and the development of quality software. These problems require solution linear systems of equations and least-square problems. The solution ...
Mar 30 2012
Solving very sparse rational systems of equations
Cook W., Steffy D. ACM Transactions on Mathematical Software 37(4): 1-21, 2011. Type: Article
This paper does exactly what its title says, in the context of linear programming. It begins with an excellent review of the literature on the subject, and then considers four main techniques: Dixon’s
Oct 26 2011
Algorithm 910: a portable C++ multiple-precision system for special-function calculations
Kormanyos C. ACM Transactions on Mathematical Software 37(4): 1-27, 2011. Type: Article
Kormanyos presents a portable C++ system for multiple precision calculations. The system supports calculations with 30 to 300 decimal digits of precision, and interoperability with Microsoft’s Common Language Runtime (CLR), Python, and...
May 23 2011
Algorithm 904: the SCASY library--parallel solvers for Sylvester-type matrix equations with applications in condition estimation, Part II
Granat R., Kågström B. ACM Transactions on Mathematical Software 37(3): 1-4, 2010. Type: Article
Sylvester-type equations occur frequently in practical applications such as control theory, signal processing, and image reduction. It is important to be able to solve these equations numerically, in an efficient and accurate manner. This paper...
Feb 1 2011
Algorithm 908: online exact summation of floating-point streams
Zhu Y., Hayes W. ACM Transactions on Mathematical Software 37(3): 1-13, 2010. Type: Article
At the innermost core of many algorithms in scientific computing is the task of summing up many floating-point numbers. Therefore, it is important to have algorithms that can handle this problem fast and accurately. A key issue in this context is ...
Dec 28 2010
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