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ACM Transactions on Mathematical Software (TOMS), Volume 25 Issue 2, June 1999

Complex fans: a representation for vectors in polar form with interval attributes
Juan Flores
Pages: 129-156
DOI: 10.1145/317275.317277
If we allow the magnitude and angle of a complex number (expressed in polar form) to range over an interval, it describes a semicircular region, similar to a fan; these regions are what we call complex fans. Complex numbers are a special case...

An interface optimization and application for the numerical solution of optimal control problems
Matthias Heinkenschloss, Luís N. Vicente
Pages: 157-190
DOI: 10.1145/317275.317278
An interface between the application problem and the nonlinear optimization algorithm is proposed for the numerical solution of distributed optimal control problems. By using this interface, numerical optimization algorithms can be designed to...

C++ classes for linking optimization with complex simulations
Mark S. Gockenbach, Matthew J. Petro, William W. Symes
Pages: 191-212
DOI: 10.1145/317275.317280
The object-oriented programming paradigm can be used to overcome the incompatibilities between off-the-shelf optimization software and application software. The Hilbert Class Library (HCL) defines the fundamental mathematical objects arising in...

Algorithm 793: GQRAT—Gauss quadrature for rational functions
Walter Gautschi
Pages: 213-239
DOI: 10.1145/317275.317282
The concern here is with Gauss-type quadrature rules that are exact for a mixture of polynomials and rational functions, the latter being selected so as to simulate poles that may be present in the integrand. The underlying theory is presented...

Algorithm 794: numerical Hankel transform by the Fortran program HANKEL
Thomas Wieder
Pages: 240-250
DOI: 10.1145/317275.317284
The numerical evaluation of the Hankel transform poses the problems of both infinite integration and Bessel function calculation. Using the corresponding numerical program routines from the literature, a Fortran program has been written to...

Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
Jan Verschelde
Pages: 251-276
DOI: 10.1145/317275.317286
Polynomial systems occur in a wide variety of application domains. Homotopy continuation methods are reliable and powerful methods to compute numerically approximations to all isolated complex solutions. During the last decade considerable...