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ACM Transactions on Mathematical Software (TOMS), Volume 32 Issue 1, March 2006

Improved long-period generators based on linear recurrences modulo 2
François Panneton, Pierre L'Ecuyer, Makoto Matsumoto
Pages: 1-16
DOI: 10.1145/1132973.1132974
Fast uniform random number generators with extremely long periods have been defined and implemented based on linear recurrences modulo 2. The twisted GFSR and the Mersenne twister are famous recent examples. Besides the period length, the statistical...

Constructing memory-minimizing schedules for multifrontal methods
Abdou Guermouche, Jean-Yves L'excellent
Pages: 17-32
DOI: 10.1145/1132973.1132975
We are interested in the memory usage of multifrontal methods. Starting from the algorithms introduced by Liu, we propose new schedules to allocate and process tasks that improve memory usage. This generalizes two existing factorization and...

Nonorthogonal decomposition of binary matrices for bounded-error data compression and analysis
Mehmet Koyutürk, Ananth Grama, Naren Ramakrishnan
Pages: 33-69
DOI: 10.1145/1132973.1132976
This article presents the design and implementation of a software tool, PROXIMUS, for error-bounded approximation of high-dimensional binary attributed datasets based on nonorthogonal decomposition of binary matrices. This tool can be used for...

Computing the real parabolic cylinder functions U(a, x), V(a, x)
Amparo Gil, Javier Segura, Nico M. Temme
Pages: 70-101
DOI: 10.1145/1132973.1132977
Methods for the computation of real parabolic cylinder functions U(a, x), and V(a, x) and their derivatives are described. We give details on power series, asymptotic series, recursion and quadrature. A...

Algorithm 850: Real parabolic cylinder functions U(a, x), V(a, x)
Amparo Gil, Javier Segura, Nico M. Temme
Pages: 102-112
DOI: 10.1145/1132973.1132978
Fortran 90 programs for the computation of real parabolic cylinder functions are presented. The code computes the functions U(a, x), V(a, x) and their derivatives for real a and x (x...

Algorithm 851: CG_DESCENT, a conjugate gradient method with guaranteed descent
William W. Hager, Hongchao Zhang
Pages: 113-137
DOI: 10.1145/1132973.1132979
Recently, a new nonlinear conjugate gradient scheme was developed which satisfies the descent condition gTkdk ≤ −7/8 ‖gk2 and...

Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
Laurent Granvilliers, Frédéric Benhamou
Pages: 138-156
DOI: 10.1145/1132973.1132980
RealPaver is an interval software for modeling and solving nonlinear systems. Reliable approximations of continuous or discrete solution sets are computed using Cartesian products of intervals. Systems are given by sets of equations or inequality...

Algorithm 853: An efficient algorithm for solving rank-deficient least squares problems
Leslie Foster, Rajesh Kommu
Pages: 157-165
DOI: 10.1145/1132973.1132981
Existing routines, such as xGELSY or xGELSD in LAPACK, for solving rank-deficient least squares problems require O(mn2) operations to solve min ‖bAx‖ where A is an m by n...

Remark on Algorithm 815: FORTRAN subroutines for computing approximate solutions of feedback set problems using GRASP
Berend Hasselman
Pages: 166-168
DOI: 10.1145/1132973.1132982
We show that the Fortran source code for Algorithm 815 contains an error and we propose a correction. The error may cause the algorithm to generate incorrect results. We also show that the performance of the corrected algorithm can be improved by a...