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ACM Transactions on Mathematical Software (TOMS), Volume 32 Issue 4, December 2006

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(n2) 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 xmki =...

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 kd 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...