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**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 *AA*^{T}*y* = *b, x* = *A*^{T}*y*. 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 *AA*^{T}, 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 R^{3} 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...