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ACM Transactions on Mathematical Software (TOMS), Volume 18 Issue 3, Sept. 1992

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...