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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
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
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...
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
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
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
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
We present a numerical procedure to approximate integrals of the form ∫baf(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
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
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.