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ACM Transactions on Mathematical Software (TOMS), Volume 41 Issue 4, October 2015

CGALmesh: A Generic Framework for Delaunay Mesh Generation
Clément Jamin, Pierre Alliez, Mariette Yvinec, Jean-Daniel Boissonnat
Article No.: 23
DOI: 10.1145/2699463

CGALmesh is the mesh generation software package of the Computational Geometry Algorithm Library (CGAL). It generates isotropic simplicial meshes—surface triangular meshes or volume tetrahedral meshes—from input surfaces, 3D domains,...

Efficient Calculations of Faithfully Rounded l2-Norms of n-Vectors
Stef Graillat, Christoph Lauter, PING Tak Peter Tang, Naoya Yamanaka, Shin’ichi Oishi
Article No.: 24
DOI: 10.1145/2699469

In this article, we present an efficient algorithm to compute the faithful rounding of the l2-norm of a floating-point vector. This means that the result is accurate to within 1 bit of the underlying floating-point type. This...

Optimizing Sparse Matrix—Matrix Multiplication for the GPU
Steven Dalton, Luke Olson, Nathan Bell
Article No.: 25
DOI: 10.1145/2699470

Sparse matrix--matrix multiplication (SpGEMM) is a key operation in numerous areas from information to the physical sciences. Implementing SpGEMM efficiently on throughput-oriented processors, such as the graphics processing unit (GPU), requires...

Algorithmic Differentiation of Numerical Methods: Tangent and Adjoint Solvers for Parameterized Systems of Nonlinear Equations
Uwe Naumann, Johannes Lotz, Klaus Leppkes, Markus Towara
Article No.: 26
DOI: 10.1145/2700820

We discuss software tool support for the algorithmic differentiation (AD), also known as automatic differentiation, of numerical simulation programs that contain calls to solvers for parameterized systems of n nonlinear equations. The local...

Algorithm 951: Cayley Analysis of Mechanism Configuration Spaces using CayMos: Software Functionalities and Architecture
Menghan Wang, Meera Sitharam
Article No.: 27
DOI: 10.1145/2699462

For a common class of two-dimensional (2D) mechanisms called 1-dof tree-decomposable linkages, we present a software package, CayMos, which uses new theoretical results from Sitharam and Wang [2014] and Sitharam et al. [2011a, 2011b] to...

Algorithm 952: PHquintic: A Library of Basic Functions for the Construction and Analysis of Planar Quintic Pythagorean-Hodograph Curves
Bohan Dong, Rida T. Farouki
Article No.: 28
DOI: 10.1145/2699467

The implementation of a library of basic functions for the construction and analysis of planar quintic Pythagorean-hodograph (PH) curves is presented using the complex representation. The special algebraic structure of PH curves permits exact...

Algorithm 953: Parallel Library Software for the Multishift QR Algorithm with Aggressive Early Deflation
Robert Granat, Bo Kågström, Daniel Kressner, Meiyue Shao
Article No.: 29
DOI: 10.1145/2699471

Library software implementing a parallel small-bulge multishift QR algorithm with Aggressive Early Deflation (AED) targeting distributed memory high-performance computing systems is presented. Starting from recent developments of the parallel...

Algorithm 954: An Accurate and Efficient Cubic and Quartic Equation Solver for Physical Applications
N. Flocke
Article No.: 30
DOI: 10.1145/2699468

We report on an accurate and efficient algorithm for obtaining all roots of general real cubic and quartic polynomials. Both the cubic and quartic solvers give highly accurate roots and place no restrictions on the magnitude of the polynomial...