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ACM Transactions on Mathematical Software (TOMS), Volume 22 Issue 3, Sept. 1996

The mathematical basis and a prototype implementation of a new polynomial rootfinder with quadratic convergence
T. E. Hull, R. Mathon
Pages: 261-280
DOI: 10.1145/232826.232830
Formulas developed originally by Weierstrass have been used since the 1960s by many others for the simultaneous determination of all the roots of a polynomial. Convergence to simple roots is quadratic, but individual approximations to a multiple...

Note on the end game in homotopy zero curve tracking
Maria Sosonkina, Layne T. Watson, David E. Stewart
Pages: 281-287
DOI: 10.1145/232826.232843
Homotopy algorithms to solve a nonlinear system of equations f(x) = 0 involve tracking the zero curve of a homotopy map p(a, &lgr;, x) from &lgr; = 0 until &lgr; = 1. When the algorithm nears or crosses the...

Algorithm 757: MISCFUN, a software package to compute uncommon special functions
Allan J. MacLeod
Pages: 288-301
DOI: 10.1145/232826.232846
MISCFUN (MISCellaneous FUNctions) is a Fortran package for the evaluation of several special functions, which are not used often enough to have been included in the standard libraries or packages. The package uses Chebyshev expansions as the...

Algorithm 758: VLUGR2: a vectorizable adaptive-grid solver for PDEs in 2D
J. G. Blom, R. A. Trompert, J. G. Verwer
Pages: 302-328
DOI: 10.1145/232826.232850
This article deals with an adaptive-grid finite-difference solver for time-dependent two-dimensional systems of partial differential equations. It describes the ANSI Fortran 77 code, VLUGR2, autovectorizable on the Cray Y-MP, that is based on...

Algorithm 759: VLUGR3: a vectorizable adaptive-grid solver for PDEs in 3D—Part II. code description
J. G. Blom, J. G. Verwer
Pages: 329-347
DOI: 10.1145/232826.232853
This article describes an ANSI Fortran 77 code, VLUGR3, autovectorizable on the Cray Y-MP, that is based on an adaptive-grid finite-difference method to solve time-dependent three-dimensional systems of partial differential equations....

A modified Schur-complement method for handling dense columns in interior-point methods for linear programming
Knud D. Andersen
Pages: 348-356
DOI: 10.1145/232826.232937
The main computational work in interior-point methods for linear programming (LP) is to solve a least-squares problem. The normal equations are often used, but if the LP constraint matrix contains a nearly dense column the normal-equations...

Algorithm 760: Rectangular-grid-data surface fitting that has the accuracy of a bicubic polynomial
Hiroshi Akima
Pages: 357-361
DOI: 10.1145/232826.232854
A local algorithm for smooth surface fitting for rectangular-grid data has been presented. It has the accuracy of a bicubic polynomial....

Algorithm 761: Scattered-data surface fitting that has the accuracy of a cubic polynomial
Hiroshi Akima
Pages: 362-371
DOI: 10.1145/232826.232856
An algorithm for smooth surface fitting for scattered data has been presented. It has the accuracy of a cubic polynomial in most cases and is a local, triangle-based algorithm....

Algorithm 762: LLDRLF, log-likelihood and some derivatives for log-F models
Barry W. Brown, Lawrence B. Levy, James Lovato, Kathy Russell, Floyd M. Spears
Pages: 372-382
DOI: 10.1145/232826.232858
The flexible statistical models incorporating the log-F distribution are little used because of numeric difficulties. We describe a method for calculating the log-likelihood and two derivatives with respect to the data argument. Fortran...