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ACM Transactions on Mathematical Software (TOMS), Volume 35 Issue 3, October 2008

Algorithms and Data Structures for Multi-Adaptive Time-Stepping
Johan Jansson, Anders Logg
Article No.: 17
DOI: 10.1145/1391989.1391990

Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the multi-adaptive...

CGMN Revisited: Robust and Efficient Solution of Stiff Linear Systems Derived from Elliptic Partial Differential Equations
Dan Gordon, Rachel Gordon
Article No.: 18
DOI: 10.1145/1391989.1391991

Given a linear system Ax  =  b, one can construct a related “normal equations” system AATy = b, x = ATy. Björck and...

Dense Linear Algebra over Word-Size Prime Fields: the FFLAS and FFPACK Packages
Jean-Guillaume Dumas, Pascal Giorgi, Clément Pernet
Article No.: 19
DOI: 10.1145/1391989.1391992

In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide...

Algorithm 885: Computing the Logarithm of the Normal Distribution
Jean Marie Linhart
Article No.: 20
DOI: 10.1145/1391989.1391993

We present and compare three C functions to compute the logarithm of the cumulative standard normal distribution. The first is a new algorithm derived from Algorithm 304’s calculation of the standard normal distribution via a series or...

Algorithm 886: Padua2D---Lagrange Interpolation at Padua Points on Bivariate Domains
Marco Caliari, Stefanode Marchi, Marco Vianello
Article No.: 21
DOI: 10.1145/1391989.1391994

We present a stable and efficient Fortran implementation of polynomial interpolation at the Padua points on the square [ − 1,1]2. These points are unisolvent and their Lebesgue constant has minimal order of growth...

Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
Yanqing Chen, Timothy A. Davis, William W. Hager, Sivasankaran Rajamanickam
Article No.: 22
DOI: 10.1145/1391989.1391995

CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AAT, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution...

Algorithm 888: Spherical Harmonic Transform Algorithms
John B. Drake, Pat Worley, Eduardo D’Azevedo
Article No.: 23
DOI: 10.1145/1391989.1404581

A collection of MATLAB classes for computing and using spherical harmonic transforms is presented. Methods of these classes compute differential operators on the sphere and are used to solve simple partial differential equations in a spherical...

Algorithm 889: Jet_fitting_3:---A Generic C++ Package for Estimating the Differential Properties on Sampled Surfaces via Polynomial Fitting
Frédéric Cazals, Marc Pouget
Article No.: 24
DOI: 10.1145/1391989.1404582

Surfaces of R3 are ubiquitous in science and engineering, and estimating the local differential properties of a surface discretized as a point cloud or a triangle mesh is a central building block in computer graphics, computer aided...