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**Sparse Matrix-Vector Multiplication on GPGPUs**

Salvatore Filippone, Valeria Cardellini, Davide Barbieri, Alessandro Fanfarillo

Article No.: 30

DOI: 10.1145/3017994

The multiplication of a sparse matrix by a dense vector (SpMV) is a centerpiece of scientific computing applications: it is the essential kernel for the solution of sparse linear systems and sparse eigenvalue problems by iterative methods. The...

**Parallel Minimum Norm Solution of Sparse Block Diagonal Column Overlapped Underdetermined Systems**

F. Sukru Torun, Murat Manguoglu, Cevdet Aykanat

Article No.: 31

DOI: 10.1145/3004280

Underdetermined systems of equations in which the minimum norm solution needs to be computed arise in many applications, such as geophysics, signal processing, and biomedical engineering. In this article, we introduce a new parallel algorithm for...

**BiqCrunch**: A Semidefinite Branch-and-Bound Method for Solving Binary Quadratic Problems

Nathan Krislock, Jérôme Malick, Frédéric Roupin

Article No.: 32

DOI: 10.1145/3005345

This article presents *BiqCrunch*, an exact solver for binary quadratic optimization problems. *BiqCrunch* is a branch-and-bound method that uses an original, efficient semidefinite-optimization-based bounding procedure. It has been...

**Chopping a Chebyshev Series**

Jared L. Aurentz, Lloyd N. Trefethen

Article No.: 33

DOI: 10.1145/2998442

Chebfun and related software projects for numerical computing with functions are based on the idea that at each step of a computation, a function *f*(*x*) defined on an interval [*a*, *b*] is “rounded” to a...

**Certified Roundoff Error Bounds Using Semidefinite Programming**

Victor Magron, George Constantinides, Alastair Donaldson

Article No.: 34

DOI: 10.1145/3015465

Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance, for FPGAs or...

**Algorithmic Differentiation of Code with Multiple Context-Specific Activities**

Jan Christian Hückelheim, Laurent Hascoët, Jens-Dominik Müller

Article No.: 35

DOI: 10.1145/3015464

Algorithmic differentiation (AD) by source-transformation is an established method for computing derivatives of computational algorithms. Static dataflow analysis is commonly used by AD tools to determine the set of *active* variables, that...

**The State-of-the-Art of Preconditioners for Sparse Linear Least-Squares Problems**

Nicholas Gould, Jennifer Scott

Article No.: 36

DOI: 10.1145/3014057

In recent years, a variety of preconditioners have been proposed for use in solving large sparse linear least-squares problems. These include simple diagonal preconditioning, preconditioners based on incomplete factorizations, and stationary inner...

**Algorithm 973**: Extended Rational Fejér Quadrature Rules Based on Chebyshev Orthogonal Rational Functions

Karl Deckers, Ahlem Mougaida, Hédi Belhadjsalah

Article No.: 37

DOI: 10.1145/3054077

We present a numerical procedure to approximate integrals of the form ∫^{b}_{a}*f*(*x*)*dx*, where *f* is a function with singularities close to, but outside the interval [*a*, *b*],...

**Algorithm 974**: The OutlierLib—A MATLAB Library for Outliers' Detection

Alexander Novoselsky, Eugene Kagan

Article No.: 38

DOI: 10.1145/3054078

The article presents a library of MATLAB functions that implement the widely used algorithms of outlier detection. The library includes the outlier tests for univariate and multivariate data sets with an approximately normal distribution. The...

**Remark on Algorithm 936**: A Fortran Message Processor

Fred T. Krogh, Richard J. Hanson, Philip W. Sharp

Article No.: 39

DOI: 10.1145/3004279

The Fortran output routine messy enables debugging and error message processing strategies in the design of numerical and mathematical software. It supports separate output from different processes in a parallel computing environment.