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Numerically Aware Orderings for Sparse Symmetric Indefinite Linear Systems
Jonathan Hogg, Jennifer Scott, Sue Thorne
Article No.: 13
Sparse symmetric indefinite problems arise in a large number of important application areas; they are often solved through the use of an LDLT factorization via a sparse direct solver. While for many problems prescaling the system...
Geometric Reconstruction of Implicitly Defined Surfaces and Domains with Topological Guarantees
Christian Engwer, Andreas Nüßing
Article No.: 14
Implicitly described domains are a well-established tool in the simulation of time-dependent problems, for example, using level-set methods. To solve partial differential equations on such domains, a range of numerical methods was developed, for...
TTC: A High-Performance Compiler for Tensor Transpositions
Paul Springer, Jeff R. Hammond, Paolo Bientinesi
Article No.: 15
We present Tensor Transpose Compiler (TTC), an open-source parallel compiler for multidimensional tensor transpositions. To generate high-performance C++ code, TTC explores a number of optimizations, including software prefetching, blocking,...
Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic
Mioara Joldes, Jean-Michel Muller, Valentina Popescu
Article No.: 15res
We analyze several classical basic building blocks of double-word arithmetic (frequently called “double-double arithmetic” in the literature): the addition of a double-word number and a floating-point number, the addition of two...
Algorithm 979: Recursive Algorithms for Dense Linear Algebra—The ReLAPACK Collection
Elmar Peise, Paolo Bientinesi
Article No.: 16
To exploit both memory locality and the full performance potential of highly tuned kernels, dense linear algebra libraries, such as linear algebra package (LAPACK), commonly implement operations as blocked algorithms. However, to achieve...
Sparse matrix factorization involves a mix of regular and irregular computation, which is a particular challenge when trying to obtain high-performance on the highly parallel general-purpose computing cores available on graphics processing units...
Algorithm 981: Talbot Suite DE: Application of Modified Talbot’s Method to Solve Differential Problems
Article No.: 18
In order to solve a differential problem, the Laplace Transform method, when applicable, replaces the problem with a simpler one; the solution is obtained by solving the new problem and then by computing the inverse Laplace Transform of...
Algorithm 982: Explicit Solutions of Triangular Systems of First-Order Linear Initial-Value Ordinary Differential Equations with Constant Coefficients
W. Van Snyder
Article No.: 19
A method to compute explicit solutions of homogeneous triangular systems of first-order linear initial-value ordinary differential equations with constant coefficients is described. It is suitable for the limited case of well separated...
Algorithm 983: Fast Computation of the Non-Asymptotic Cochran’s Q Statistic for Heterogeneity Detection
Thierry Fahmy, Arnaud Bellétoile
Article No.: 20
The detection of heterogeneity among objects (products, treatments, medical studies) assessed on a series of blocks (consumers, patients, methods, pathologists) is critical in numerous areas such as clinical research, cosmetic...
Algorithm 984: ADiGator, a Toolbox for the Algorithmic Differentiation of Mathematical Functions in MATLAB Using Source Transformation via Operator Overloading
Matthew J. Weinstein, Anil V. Rao
Article No.: 21
A toolbox called ADiGator is described for algorithmically differentiating mathematical functions in MATLAB. ADiGator performs source transformation via operator overloading using forward mode algorithmic differentiation and produces a file that...
Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the Faddeyeva Function
Mofreh R. Zaghloul
Article No.: 22
We present a new simple algorithm for efficient, and relatively accurate computation of the Faddeyeva function w(z). The algorithm carefully exploits previous approximations by Hui et al. (1978) and Humlíček (1982)...
Algorithm 986: A Suite of Compact Finite Difference Schemes
Mani Mehra, Kuldip Singh Patel
Article No.: 23
A collection of Matlab routines that compute derivative approximations of arbitrary functions using high-order compact finite difference schemes is presented. Tenth-order accurate compact finite difference schemes for first and second derivative...