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ACM Transactions on Mathematical Software (TOMS), Volume 18 Issue 2, June 1992

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints
R. J. Hanson, Fred T. Krogh
Pages: 115-133
DOI: 10.1145/146847.146857
A new algorithm is presented for solving nonlinear least-squares and nonlinear equation problems. The algorithm is based on approximating the nonlinear functions using the quadratic-tensor model proposed by Schnabel and Frank. The problem...

A test for cancellation errors in quasi-Newton methods
Chaya Gurwitz
Pages: 134-140
DOI: 10.1145/146847.146876
It has recently been shown that cancellation errors in a quasi-Newton method can increase without bound as the method converges. A simple test is presented to determine when cancellation errors could lead to significant contamination of the...

Algorithm 702: TNPACK–a truncated Newton minimization package for large-scale problems: I. Algorithm and usage
Tamar Schlick, Aaron Fogelson
Page: 141
DOI: 10.1145/146847.146921
We present a FORTRAN package of subprograms for minimizing multivariate functions without constraints by a truncated Newton algorithm. The algorithm is especially suited for problems involving a large number of variables. Truncated Newton...

An MEBDF code for stiff initial value problems
J. R. Cash, S. Considine
Pages: 142-155
DOI: 10.1145/146847.146922
In two recent papers one of the present authors has proposed a class of modified extended backward differentiation formulae for the numerical integration of stiff initial value problems. In this paper we describe a code based on this class of...

Algorithm 703: MEBDF: a FORTRAN subroutine for solving first-order systems of stiff initial value problems for ordinary differential equations
J. R. Cash, S. Considine
Pages: 156-158
DOI: 10.1145/146847.146923

An efficient method for the numerical evaluation of partial derivatives of arbitrary order
Richard D. Neidinger
Pages: 159-173
DOI: 10.1145/146847.146924
For any typical multivariable expression f, point a in the domain of f, and positive integer maxorder, this method produces the numerical values of all partial derivatives at a...

Exact equations of the nonlinear spline
John A. Edwards
Pages: 174-192
DOI: 10.1145/146847.146925
We define the spline interpolating function, and obtain in directly computable form the elementary set of nonlinear equations describing nonlinear spline curves. Using Newton's and Newton-like methods, we solve typical spline configurations, and...

The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions
Gouad Majaess, Patrick Keast, Graeme Fairweather, Karin R. Bennett
Pages: 193-204
DOI: 10.1145/146847.146926
Numerical techniques based on piecewise polynomial (that is, spline) collation at Gaussian points are exceedingly effective for the approximate solution of boundary value problems, both for ordinary differential equations and for time dependent...

Algorithm 704: ABDPACK and ABBPACK-FORTRAN programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions
Fouad Majaess, Patrick Keast, Graeme Fairweather, Karin R. Bennett
Pages: 205-210
DOI: 10.1145/146847.146927
ABDPACK is a package of FORTRAN programs for the solution of systems of linear equations with the almost block diagonal structure arising in spline collocation at Gaussian points with monomial spline basis functions, when applied to two-point...

Table-driven implementation of the Expm1 function in IEEE floating-point arithmetic
Ping Tak Peter Tang
Pages: 211-222
DOI: 10.1145/146847.146928
Algorithms and implementation details for the function ex - 1 in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the...

Solution of the Sylvester matrix equation AXBT + CXDT = E
Judith D. Gardiner, Alan J. Laub, James J. Amato, Cleve B. Moler
Pages: 223-231
DOI: 10.1145/146847.146929
A software package has been developed to solve efficiently the Sylvester-type matrix equation AXBT + CXDT = E. A transformation method is used which...

Algorithm 705; a FORTRAN-77 software package for solving the Sylvester matrix equation AXBT + CXDT = E
Judith D. Gardiner, Matthew R. Wette, Alan J. Laub, James J. Amato, Cleve B. Moler
Pages: 232-238
DOI: 10.1145/146847.146930
This paper documents a software package for solving the Sylvester matrix equation (1) AXBT + CXDT = e All quantities are real matrices;...