**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...