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ACM Transactions on Mathematical Software (TOMS), Volume 23 Issue 3, Sept. 1997

Implementing the complex arcsine and arccosine functions using exception handling
T. E. Hull, Thomas F. Fairgrieve, Ping Tak Peter Tang
Pages: 299-335
DOI: 10.1145/275323.275324
We develop efficient algorithms for reliable and accurate evaluatins of the complex arcsine and arccosine functions. A tight error bound is derived for each algorithm; the results are valid for all machine-representable points in the complex...

Compiler blockability of dense matrix factorizations
Steve Carr, R. B. Lehoucq
Pages: 336-361
DOI: 10.1145/275323.275325
The goal of the LAPACK project is to provide efficient and portable software for dense numerical linear algebra computations. By recasting many of the fundamental dense matrix computations in terms of calls to an efficient implementation of the...

Efficient householder QR factorization for superscalar processors
James J. Carrig, Jr., Gerard G. L. Meyer
Pages: 362-378
DOI: 10.1145/275323.275326
To extract the potential promised by superscalar processors, algorithm designers must streamline memory references and allow for efficient data reuse throughout the memory hierarchy. Two parameterized Householder QR factorization algorithms are...

Level 3 basic linear algebra subprograms for sparse matrices: a user-level interface
Iain S. Duff, Michele Marrone, Giuseppe Radicati, Carlo Vittoli
Pages: 379-401
DOI: 10.1145/275323.275327
This article proposes a set of Level 3 Basic Linear Algebra Subprograms and associated kernels for sparse matrices. A major goal is to design and develop a common framework to enable efficient, and portable, implementations of iterative...

Algorithm 771: rksuite_90: Fortran 90 software for ordinary differential equation initial-value problems
R. W. Brankin, I. Gladwell
Pages: 402-415
DOI: 10.1145/275323.275328
The present Fortran 90 software for the initial-value problem in ordinary differential equations including the interfaces and how Fortran 90 language features afford the opportunity both to address different types and structures of variables and...

Algorithm 772: STRIPACK: Delaunay triangulation and Voronoi diagram on the surface of a sphere
Robert J. Renka
Pages: 416-434
DOI: 10.1145/275323.275329
STRIPACK is a Fortran 77 software package that employs an incremental algorithm to construct a Delaunay triangulation and, optionally, a Voronoi diagram of a set of points (nodes) on the surface of the unit sphere. The triangulation covers the...

Algorithm 773: SSRFPACK: interpolation of scattered data on the surface of a sphere with a surface under tension
Robert J. Renka
Pages: 435-442
DOI: 10.1145/275323.275330
SSRFPACK is a Fortran 77 software package that constructs a smooth interpolatory or approximating surface to data values associated with arbitrarily distributed points on the surface of a sphere. It employs automatically selected tension factors...

Generating box-constrained optimization problems
Francisco Facchinei, Joaquim Júdice, João Soares
Pages: 443-447
DOI: 10.1145/275323.275331
We present a method for generating box-constrained nonlinear programming test problems. The technique allows the user to control some properties of the generated test problems that are know to influence the behavior of algorithms for their...

Algorithm 774: Fortran subroutines for generating box-constrained optimization problems
Francisco Facchinei, Joaquim Júdice, João Soares
Pages: 448-450
DOI: 10.1145/275323.275332
We describe a set of Fortran routines for generatig box-constrained nonlinear programming test problems. The technique, as described by Facchinei et al. (this issue), allows the user to control relevant properties of the generated problems...