test_nonlin
test_nonlin,
a Python code which
defines a set of test problems for nonlinear
equation system solvers.
A few of the problems are small (2, 3, or 4 equations in 4
unknowns), but most of the problems may be set to any size whatsoever.
The software includes routines defining the initial approximation to the
solution of the system, the N function values at any point, and the N by
N jacobian matrix at any point.
The list of problems includes:
-
Generalized Rosenbrock function, 1 < N.
-
Powell singular function, N = 4.
-
Powell badly scaled function, N = 2.
-
Wood function, N = 4.
-
Helical valley function, N = 3.
-
Watson function, 1 < N.
-
Chebyquad function, N arbitrary.
-
Brown almost linear function, N arbitrary.
-
Discrete boundary value function, N arbitrary.
-
Discrete integral equation function, N arbitrary.
-
Trigonometric function, N arbitrary.
-
Variably dimensioned function, N arbitrary.
-
Broyden tridiagonal function, N arbitrary.
-
Broyden banded function, N arbitrary.
-
Hammarling 2 by 2 matrix square root problem, N = 4.
-
Hammarling 3 by 3 matrix square root problem, N = 9.
-
Dennis and Schnabel example, N = 2.
-
Sample problem 18, N = 2.
-
Sample problem 19, N = 2.
-
Scalar problem, N = 1.
-
Freudenstein-Roth function, N = 2.
-
Boggs function, N = 2.
-
Chandrasekhar function, N arbitrary.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license
Languages:
test_nonlin is available in
a FORTRAN90 version and
a MATLAB version and
an Octave version and
a Python version.
Related Data and Programs:
fsolve_test,
a Python code which
calls fsolve() which
seeks the solution x of one or more nonlinear equations f(x)=0.
test_zero,
a Python code which
implements test problems for the solution
of a single nonlinear equation in one variable.
Reference:
-
Subramanyan Chandrasekhar,
Radiative Transfer,
Dover, 1960,
ISBN13: 978-0486605906,
LC: QB461.C46.
-
John Dennis, David Gay, Phuong Vu,
A new nonlinear equations test problem,
Technical Report 83-16,
Mathematical Sciences Department,
Rice University, 1983.
-
John Dennis, Robert Schnabel,
Numerical Methods for Unconstrained Optimization
and Nonlinear Equations,
SIAM, 1996,
ISBN13: 978-0-898713-64-0,
LC: QA402.5.D44.
-
Noel deVilliers, David Glasser,
A continuation method for nonlinear regression,
SIAM Journal on Numerical Analysis,
Volume 18, Number 6, December 1981, pages 1139-1154.
-
Chris Fraley,
Solution of nonlinear least-squares problems,
Technical Report STAN-CS-1165,
Computer Science Department,
Stanford University, 1987.
-
Chris Fraley,
Software performance on nonlinear least-squares problems,
Technical Report SOL 88-17,
Systems Optimization Laboratory,
Department of Operations Research,
Stanford University, 1988.
-
JJ McKeown,
Specialized versus general-purpose algorithms for functions
that are sums of squared terms,
Mathematical Programming,
Volume 9, 1975, pages 57-68.
-
JJ McKeown,
On algorithms for sums of squares problems,
in Towards Global Optimisation,
edited by Laurence Dixon, Gabor Szego,
North-Holland, 1975, pages 229-257,
ISBN: 0444109552,
LC: QA402.5.T7.
-
Jorge More, Burton Garbow, Kenneth Hillstrom,
Testing unconstrained optimization software,
ACM Transactions on Mathematical Software,
Volume 7, Number 1, March 1981, pages 17-41.
-
Jorge More, Burton Garbow, Kenneth Hillstrom,
Algorithm 566:
FORTRAN Subroutines for Testing unconstrained optimization software,
ACM Transactions on Mathematical Software,
Volume 7, Number 1, March 1981, pages 136-140.
-
James Ortega, Werner Rheinboldt
Iterative Solution of Nonlinear Equations in Several Variables,
SIAM, 1987,
ISBN13: 978-0898714616,
LC: QA297.8.O77.
-
Werner Rheinboldt,
Methods for Solving Systems of Nonlinear Equations,
SIAM, 1998,
ISBN: 089871415X,
LC: QA214.R44.
-
Douglas Salane,
A continuation approach for solving large residual nonlinear
least squares problems,
SIAM Journal on Scientific and Statistical Computing,
Volume 8, Number 4, July 1987, pages 655-671.
Source Code:
Individual test problems:
Last revised on 16 October 2020.