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On BLAS level3 implementations of common solvers for (quasi) triangular generalized Lyapunov equations
Köhler M., Saak J. ACM Transactions on Mathematical Software 43(1): 123, 2016. Type: Article
Each of the generalized Lyapunov matrix equations can be seen simply as a system of linear equations in the elements of the unknown matrix
X
. For numerical solutions, however, it is usually kept in its matrix form. The continuou...
Oct 20 2016
A high performance QDWHSVD solver using hardware accelerators
Sukkari D., Ltaief H., Keyes D. ACM Transactions on Mathematical Software 43(1): 125, 2016. Type: Article
To make effective use of modern computer hardware, algorithms have to be carefully designed with concurrency in mind: in particular, they need to efficiently utilize the multiple cores provided by the computer’s generalpurpose central proce...
Oct 20 2016
Algorithm 958: Lattice Builder: a general software tool for constructing rank1 lattice rules
L’ecuyer P., Munger D. ACM Transactions on Mathematical Software 42(2): 130, 2016. Type: Article
The problem of numerically integrating multidimensional functions arises from function approximation, optimization, and solving partial differential equations, among others. The number of function evaluations, the major cost of numerical integrati...
Jul 22 2016
Algorithm 957: evaluation of the repeated integral of the coerror function by halfrange GaussHermite quadrature
Gautschi W. ACM Transactions on Mathematical Software 42(1): 110, 2016. Type: Article
The accurate evaluation of the repeated integrals of the coerror function defined as
with
is required in a number of...
Jun 24 2016
Testing matrix function algorithms using identities
Deadman E., Higham N. ACM Transactions on Mathematical Software 42(1): 115, 2016. Type: Article
Functional identity can be analyzed using reference solutions or with the Python library SciPy module that contains many probability distributions, one of which is a roundtrip stability test of the algorithms. Linearized backward error can be com...
Jun 17 2016
Algorithm 954: an accurate and efficient cubic and quartic equation solver for physical applications
Flocke N. ACM Transactions on Mathematical Software 41(4): 124, 2015. Type: Article
Flocke developed an algorithm for obtaining all the zeros of cubic and quartic polynomials. The key to accuracy is scaling the polynomials so that all coefficients in absolute value are bounded by unity. A recent book by Boyd [1] contains a chapte...
Dec 1 2015
Computing petaflops over terabytes of data: the case of genomewide association studies
FabregatTraver D., Bientinesi P. ACM Transactions on Mathematical Software 40(4): 122, 2014. Type: Article
With its catchy but somewhat misleading title, this paper proposes a method for efficiently solving multiple instances of the same problem when the instances are correlated....
Oct 16 2014
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 t...
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 for...
Aug 16 2013
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