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**A parallel direct solver for large sparse highly unsymmetric linear systems**

Iain S. Duff, Jennifer A. Scott

Pages: 95-117

DOI: 10.1145/992200.992201

The need to solve large sparse linear systems of equations efficiently lies at the heart of many applications in computational science and engineering. For very large systems when using direct factorization methods of solution, it can be beneficial...

**MA57---a code for the solution of sparse symmetric definite and indefinite systems**

Iain S. Duff

Pages: 118-144

DOI: 10.1145/992200.992202

We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with 2 × 2 pivoting for stability. This code, called MA57, is in HSL 2002 and supersedes the well used HSL code MA27. We...

**Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments**

Amparo Gil, Javier Segura, Nico M. Temme

Pages: 145-158

DOI: 10.1145/992200.992203

We describe a variety of methods to compute the functions *K*_{ia}(*x*), *L*_{ia}(*x*) and their derivatives for real *a* and positive *x*. These functions are numerically satisfactory...

**Algorithm 831**: Modified Bessel functions of imaginary order and positive argument

Amparo Gil, Javier Segura, Nico M. Temme

Pages: 159-164

DOI: 10.1145/992200.992204

Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions *K*_{ia}(*x*), *L*_{ia}(*x*) and their derivatives for...

**A column pre-ordering strategy for the unsymmetric-pattern multifrontal method**

Timothy A. Davis

Pages: 165-195

DOI: 10.1145/992200.992205

A new method for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The column ordering is selected to give a good a priori upper bound on...

**Algorithm 832**: UMFPACK V4.3---an unsymmetric-pattern multifrontal method

Timothy A. Davis

Pages: 196-199

DOI: 10.1145/992200.992206

An ANSI C code for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The pre-ordering and symbolic analysis phase computes an upper bound...

**Algorithm 833**: CSRFPACK---interpolation of scattered data with a *C*^{1} convexity-preserving surface

Robert J. Renka

Pages: 200-211

DOI: 10.1145/992200.992207

We describe a Fortran-77 software package for constructing a *C*^{1} convex surface that interpolates a convex data set consisting of data values at arbitrarily distributed points in the plane (nodes) such that there exists a...

**Algorithm 834**: glsurf---an interactive surface plotting program using OpenGL

Robert J. Renka

Pages: 212-217

DOI: 10.1145/992200.992208

We describe an interactive surface visualization tool implemented in C, OpenGL, and GLUT. The surface is represented by a set of triangles in Euclidean 3-space, thus allowing for unrestricted topology. Capabilities include color-filled contour plots...

**Algorithm 835**: MultRoot---a Matlab package for computing polynomial roots and multiplicities

Zhonggang Zeng

Pages: 218-236

DOI: 10.1145/992200.992209

MultRoot is a collection of Matlab modules for accurate computation of polynomial roots, especially roots with non-trivial multiplicities. As a blackbox-type software, MultRoot requires the polynomial coefficients as the only input, and outputs the...