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ACM Transactions on Mathematical Software (TOMS), Volume 21 Issue 4, Dec. 1995

A modification of Talbot's method for the simultaneous approximation of several values of the inverse Laplace transform
Mariarosaria Rizzardi
Pages: 347-371
DOI: 10.1145/212066.212068
In recent years many results have been obtained in the field of the numerical inversion of Laplace transforms. Among them, a very accurate and general method is due to Talbot: this method approximates the value of the inverse Laplace transform...

Algorithm 749: fast discrete cosine transform
Barry G. Sherlock, Donald M. Monro
Pages: 372-378
DOI: 10.1145/212066.212071
An in-place algorithm for the fast, direct computation of the forward and inverse discrete cosine transform is presented and evaluated. The transform length may be an arbitrary power of two.

A Fortran 90-based multiprecision system
David H. Bailey
Pages: 379-387
DOI: 10.1145/212066.212075
A new version of a Fortran multiprecision computation system, based on the Fortran 90 language, is described. With this new approach, a translator program is not required—translation of Fortran code for multiprecision is accomplished by...

A remark on Algorithm 644: “A portable package for Bessel functions of a complex argument and nonnegative order”
D. E. Amos
Pages: 388-393
DOI: 10.1145/212066.212078
Algorithm 644 computes all major Bessel functions of a complex argument and of nonnegative order. Single-precision routine CBESY and double-precision routine ZBESY are modified to reduce the computation time for the Y Bessel...

Exact solution of large-scale, asymmetric traveling salesman problems
G. Carpaneto, M. Dell'Amico, P. Toth
Pages: 394-409
DOI: 10.1145/212066.212081
A lowest-first, branch-and-bound algorithm for the Asymmetric Traveling Salesman Problem is presented. The method is based on the Assignment Problem relaxation and on a subtour elimination branching...

Algorithm 750: CDT: a subroutine for the exact solution of large-scale, asymmetric traveling salesman problems
G. Carpaneto, M. Dell'Amico, P. Toth
Pages: 410-415
DOI: 10.1145/212066.212084
The Fortran code CDT, implementing an algorithm for the asymmetric traveling salesman problem, is presented. The method is based on the Assignment Problem relaxation and on a subtour elimination...

A set of Ada packages for high-precision calculations
B. G. S. Doman, C. J. Pursglove, W. M. Coen
Pages: 416-431
DOI: 10.1145/212066.212087
The packages described here are designed to perform efficient high-accuracy calculations in cases where there can be serious loss of significance due to rounding errors. Numbers are represented by a value part with a variable number of digits in...

An Arnoldi code for computing selected eigenvalues of sparse, real, unsymmetric matrices
Jennifer A. Scott
Pages: 432-475
DOI: 10.1145/212066.212091
Arnoldi methods can be more effective than subspace iteration methods for computing the dominant eigenvalues of a large, sparse, real, unsymmetric matrix. A code, EB12, for the sparse, unsymmetric eigenvalue...

Computing the MDMT decomposition
Linda Kaufman
Pages: 476-489
DOI: 10.1145/212066.212092
The MDMT factorization of an n×n symmetric indefinite matrix A can be used to solve a linear system with A as the coefficient matrix. This...

Corrigendum: Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration
I. S. Duff, J. A. Scott
Page: 490
DOI: 10.1145/212066.215254