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**Robust and reliable defect control for Runge-Kutta methods**

W. H. Enright, Wayne B. Hayes

Article No.: 1

DOI: 10.1145/1206040.1206041

The quest for reliable integration of *initial value problems* (IVPs) for *ordinary differential equations* (ODEs) is a long-standing problem in numerical analysis. At one end of the reliability spectrum are fixed stepsize methods...

**Complex standard functions and their implementation in the CoStLy library**

Markus Neher

Article No.: 2

DOI: 10.1145/1206040.1206042

The practical calculation of range bounds for some complex standard functions is addressed in this article. The functions under consideration are root and power functions, the exponential, trigonometric and hyperbolic functions, and their inverse...

**FILTRANE, a Fortran 95 filter-trust-region package for solving nonlinear least-squares and nonlinear feasibility problems**

Nicholas I. M. Gould, Philippe L. Toint

Article No.: 3

DOI: 10.1145/1206040.1206043

FILTRANE, a new Fortran 95 package for finding vectors satisfying general sets of nonlinear equations and/or inequalities, is presented. Several algorithmic variants are discussed and extensively compared on a set of CUTEr test problems,...

**EXPINT---A MATLAB package for exponential integrators**

Håvard Berland, Bård Skaflestad, Will M. Wright

Article No.: 4

DOI: 10.1145/1206040.1206044

Recently, a great deal of attention has been focused on the construction of exponential integrators for semilinear problems. In this article we describe a MATLAB^{1} package which aims to facilitate the quick deployment and testing of...

**Using dense storage to solve small sparse linear systems**

Marco Morandini, Paolo Mantegazza

Article No.: 5

DOI: 10.1145/1206040.1206045

A data structure is used to build a linear solver specialized for relatively small sparse systems. The proposed solver, optimized for run-time performance at the expense of memory footprint, outperforms widely used direct and sparse solvers for...

**Algorithm 863**: L2WPMA, a Fortran 77 package for weighted least-squares piecewise monotonic data approximation

Ioannis C. Demetriou

Article No.: 6

DOI: 10.1145/1206040.1206046

Fortran software is developed that calculates a best piecewise monotonic approximation to *n* univariate data contaminated by random errors. The underlying method minimizes the weighted sum of the squares of the errors by requiring *k*...

**Algorithm 864**: General and robot-packable variants of the three-dimensional bin packing problem

Silvano Martello, David Pisinger, Daniele Vigo, Edgar Den Boef, Jan Korst

Article No.: 7

DOI: 10.1145/1206040.1206047

We consider the problem of orthogonally packing a given set of rectangular-shaped boxes into the minimum number of three-dimensional rectangular bins. The problem is NP-hard in the strong sense and extremely difficult to solve in practice. We...

**Algorithm 865**: Fortran 95 subroutines for Cholesky factorization in block hybrid format

Fred G. Gustavson, John K. Reid, Jerzy Waśniewski

Article No.: 8

DOI: 10.1145/1206040.1206048

We present subroutines for the Cholesky factorization of a positive-definite symmetric matrix and for solving corresponding sets of linear equations. They exploit cache memory by using the block hybrid format proposed by the authors in a companion...