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**Inverting the symmetrical beta distribution**

Pierre L'Ecuyer, Richard Simard

Pages: 509-520

DOI: 10.1145/1186785.1186786

We propose a fast algorithm for computing the inverse symmetrical beta distribution. Four series (two around *x* = 0 and two around *x* = 1/2) are used to approximate the distribution function, and its inverse is found via...

**Block algorithms for reordering standard and generalized Schur forms**

Daniel Kressner

Pages: 521-532

DOI: 10.1145/1186785.1186787

Block algorithms for reordering a selected set of eigenvalues in a standard or generalized Schur form are proposed. Efficiency is achieved by delaying orthogonal transformations and (optionally) making use of level 3 BLAS operations. Numerical...

**The design and implementation of the MRRR algorithm**

Inderjit S. Dhillon, Beresford N. Parlett, Christof Vömel

Pages: 533-560

DOI: 10.1145/1186785.1186788

In the 1990's, Dhillon and Parlett devised the algorithm of multiple relatively robust representations (MRRR) for computing numerically orthogonal eigenvectors of a symmetric tridiagonal matrix *T* with O(n^{2}) cost. While previous...

**Algorithm 857**: POLSYS_GLP—a parallel general linear product homotopy code for solving polynomial systems of equations

Hai-Jun Su, J. Michael McCarthy, Masha Sosonkina, Layne T. Watson

Pages: 561-579

DOI: 10.1145/1186785.1186789

Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one...

**Algorithm 858**: Computing infinite range integrals of an arbitrary product of Bessel functions

Joris Van Deun, Ronald Cools

Pages: 580-596

DOI: 10.1145/1186785.1186790

We present an algorithm to compute integrals of the form ∫^{∞}_{0} *x*^{m} ∏^{k}_{i} =...

**Algorithm 859**: BABDCR—a Fortran 90 package for the solution of bordered ABD linear systems

Pierluigi Amodio, Giuseppe Romanazzi

Pages: 597-608

DOI: 10.1145/1186785.1186791

BABDCR is a package of Fortran 90 subroutines for the solution of linear systems with bordered almost block diagonal coefficient matrices. It is designed to handle matrices with blocks of the same size, that is, having a block upper bidiagonal...

**Algorithm 860**: SimpleS—an extension of Freudenthal's simplex subdivision

Eduardo N. Gonçalves, Reinaldo M. Palhares, Ricardo H. C. Takahashi, Renato C. Mesquita

Pages: 609-621

DOI: 10.1145/1186785.1186792

This article presents a simple efficient algorithm for the subdivision of a *d*-dimensional simplex in *k*^{d} simplices, where *k* is any positive integer number. The algorithm is an extension of Freudenthal's...

**Algorithm 861**: Fortran 90 subroutines for computing the expansion coefficients of Mathieu functions using Blanch's algorithm

Danilo Erricolo

Pages: 622-634

DOI: 10.1145/1186785.1186793

A translation to Fortran 90 of Gertrude Blanch's algorithm for computing the expansion coefficients of the series that represent Mathieu functions is presented. Its advantages are portability, higher precision, practicality of use, and extended...

**Algorithm 862**: MATLAB tensor classes for fast algorithm prototyping

Brett W. Bader, Tamara G. Kolda

Pages: 635-653

DOI: 10.1145/1186785.1186794

Tensors (also known as multidimensional arrays or *N*-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm...