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**Numerically Aware Orderings for Sparse Symmetric Indefinite Linear Systems**

Jonathan Hogg, Jennifer Scott, Sue Thorne

Article No.: 13

DOI: 10.1145/3104991

Sparse symmetric indefinite problems arise in a large number of important application areas; they are often solved through the use of an *LDL ^{T}* 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

DOI: 10.1145/3104989

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

DOI: 10.1145/3104988

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

DOI: 10.1145/3121432

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

DOI: 10.1145/3061664

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...

**Algorithm 980**: Sparse QR Factorization on the GPU

Sencer Nuri Yeralan, Timothy A. Davis, Wissam M. Sid-Lakhdar, Sanjay Ranka

Article No.: 17

DOI: 10.1145/3065870

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

Mariarosaria Rizzardi

Article No.: 18

DOI: 10.1145/3089248

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

DOI: 10.1145/3092892

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

DOI: 10.1145/3095076

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

DOI: 10.1145/3104990

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

DOI: 10.1145/3119904

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

DOI: 10.1145/3119905

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...