**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