**A portable code generator for CRAY FORTRAN**

Sanjiva Weerawarana, Paul S. Wang

Pages: 241-255

DOI: 10.1145/131766.131767

One way to combine the powers of symbolic computing with numeric computing is to automaticaly derive and produce numeric code. This approach has important applications in science and engineering. Once the desired formulas and procedures are...

**FORTRAN subroutines for general Toeplitz systems**

Per Christian Hansen, Tony F. Chan

Pages: 256-273

DOI: 10.1145/131766.131768

This paper presents FORTRAN 77 implementations of the lookahead Levinson algorithm of Chan and Hansen [7, 8] for solving symmetric indefinite and general Toeplitz systems. The algorithms are numerically stable for all Toeplitz matrices that do...

**Stability of block algorithms with fast level-3 BLAS**

James W. Demmel, Nicholas J. Higham

Pages: 274-291

DOI: 10.1145/131766.131769

Block algorithms are becoming increasingly popular in matrix computations. Since their basic unit of data is a submatrix rather than a scalar, they have a higher level of granularity than point algorithms, and this makes them well suited to...

**An implementation of a divide and conquer algorithm for the unitary eigen problem**

G. S. Ammar, L. Reichel, D. C. Sorensen

Pages: 292-307

DOI: 10.1145/131766.131770

We present a FORTRAN implementation of a divide-and-conquer method
for computing the spectral resolution of a unitary upper Hessenberg
matrix H. Any such matrix
H of order...

**LSNNO, a FORTRAN subroutine for solving large-scale nonlinear network optimization problems**

Ph. L. Toint, D. Tuyttens

Pages: 308-328

DOI: 10.1145/131766.131771

The implementation and testing of LSNNO, a new FORTRAN subroutine for solving large-scale nonlinear network optimization problems is described. The implemented algorithm applies the concepts of partial separability and partitioned quasi-Newton...

**Algorithm 706: DCUTRI: an algorithm for adaptive cubature over a collection of triangles**

Jarle Berntsen, Terje O. Espelid

Pages: 329-342

DOI: 10.1145/131766.131772

An adaptive algorithm for computing an approximation to the integral of each element in a vector function f(x,y) over a two-dimensional region made up of triangles is presented. A FORTRAN implementation of the algorithm is...

**Remark on algorithm 540**

Tim Hopkins

Pages: 343-344

DOI: 10.1145/131766.131773

**Algorithm 707: CONHYP: a numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes**

Mark Nardin, W. F. Perger, Atul Bhalla

Pages: 345-349

DOI: 10.1145/131766.131774

A numerical evaluator for the confluent hypergeometric function for complex arguments with large magnitudes using a direct summation of Kummer's series is presented. Extended precision subroutines using large arrays to accumulate a single...

**Real zero isolation for trigonometric polynomials**

Achim Schweikard

Pages: 350-359

DOI: 10.1145/131766.131775

An exact and practical method for determining the number, location, and multiplicity of all real zeros of the trigonometric polynomials is described. All computations can be performed without loss of accuracy. lThe method is based on zero...

**Algorithm 708: Significant digit computation of the incomplete beta function ratios**

Armido R. Didonato, Alfred H. Morris, Jr.

Pages: 360-373

DOI: 10.1145/131766.131776

An algorithm is given for evaluating the incomplete beta function ratio Ix(a,b) and its complement 1 - Ix(a,b). A new continued fraction and a new asymptotic series are...