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**The complex-step derivative approximation**

Joaquim R. R. A. Martins, Peter Sturdza, Juan J. Alonso

Pages: 245-262

DOI: 10.1145/838250.838251

The complex-step derivative approximation and its application to numerical algorithms are presented. Improvements to the basic method are suggested that further increase its accuracy and robustness and unveil the connection to algorithmic...

**ACETAF**: A software package for computing validated bounds for Taylor coefficients of analytic functions

Ingo Eble, Markus Neher

Pages: 263-286

DOI: 10.1145/838250.838252

This article presents methods for practical computation of verified bounds for Taylor coefficients of analytic functions. These bounds are constructed from Cauchy's estimate and from some of its modifications. Interval arithmetic is used to obtain...

**Algorithm 824**: *CUBPACK*: a package for automatic cubature; framework description

Ronald Cools, Ann Haegemans

Pages: 287-296

DOI: 10.1145/838250.838253

CUBPACK aims to offer a collection of re-usable code for automatic *n*-dimensional (*n* ≥ 1) numerical integration of functions over a collection of regions, i.e., quadrature and cubature. The current version allows this region to...

**An adaptive numerical cubature algorithm for simplices**

Alan Genz, Ronald Cools

Pages: 297-308

DOI: 10.1145/838250.838254

A globally adaptive algorithm for numerical cubature of a vector of functions over a collection of *n*-dimensional simplices is described. The algorithm is based on a subdivision strategy that chooses for subdivision at each stage the subregion...

**Algorithm 825**: A deep-cut bisection envelope algorithm for fixed points

Spencer Shellman, K. Sikorski

Pages: 309-325

DOI: 10.1145/838250.838255

We present the BEDFix (Bisection Envelope Deep-cut Fixed point) algorithm for the problem of approximating a fixed point of a function of two variables. The function must be Lipschitz continuous with constant 1 with respect to the infinity norm; such...

**Algorithm 826**: A parallel eigenvalue routine for complex Hessenberg matrices

Mark R. Fahey

Pages: 326-336

DOI: 10.1145/838250.838256

A code for computing the eigenvalues of a complex Hessenberg matrix is presented. This code computes the Schur decomposition of a complex Hessenberg matrix. Together with existing ScaLAPACK routines, the eigenvalues of dense complex matrices can be...

**Algorithm 827**: irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix

J. Baglama, D. Calvetti, L. Reichel

Pages: 337-348

DOI: 10.1145/838250.838257

irbleigs is a MATLAB program for computing a few eigenvalues and associated eigenvectors of a sparse Hermitian matrix of large order *n*. The matrix is accessed only through the evaluation of matrix-vector products. Working space of only a few...

**Remark on Algorithm 769**: Fortran subroutines for approximate solution of sparse quadratic assignment problems using GRASP

Tim Hopkins

Pages: 349-351

DOI: 10.1145/838250.838258

We present a number of corrections and improvements to Algorithm 769 [Pardalos et al. 1997].