TEST_CON
Continuation Data

TEST_CON is a dataset directory which is associated with the sample continuation problems in the TEST_CON software library.

The TEST_CON software library defines 19 problems, some of them with several options. Each problem and option defines a nonlinear set of functions with one degree of freedom. The solutions of this function lie on a curve. Continuation codes try to produce a series of points on such a curve.

For some of the nonlinear functions defined by TEST_CON software, this directory has a corresponding directory containing points X and tangent vectors T(X) representing a series of solutions on the curve. This data can be used for plotting, or for comparison with results obtained by other programs.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

PITCON66, a FORTRAN77 library which seeks to produce a sequence of points that satisfy a set of nonlinear equations with one degree of freedom; this is version 6.6 of ACM TOMS algorithm 596.

PITCON7, a FORTRAN90 library which seeks to produce a sequence of points that satisfy a set of nonlinear equations with one degree of freedom; this is version 7.0 of ACM TOMS algorithm 596.

TEST_CON, a FORTRAN90 library which implements test problems for numerical continuation.

TEST_CON, a MATLAB library which implements test problems for numerical continuation.

TOMS502, a FORTRAN77 library which seeks to produce a sequence of points that satisfy a set of nonlinear equations with one degree of freedom; this library is commonly called DERPAR;
this is ACM TOMS algorithm 502.

TOMS596, a FORTRAN77 library which seeks to produce a sequence of points that satisfy a set of nonlinear equations with one degree of freedom; this library is commonly called PITCON;
this is ACM TOMS algorithm 596.

Reference:

1. Rami Melhem, Werner Rheinboldt,
   A Comparison of Methods for Determining Turning Points of Nonlinear Equations,
   Computing,
   Volume 29, Number 3, September 1982, pages 201-226.
2. Werner Rheinboldt,
   Computation of Critical Boundaries on Equilibrium Manifolds,
   SIAM Journal on Numerical analysis,
   Volume 19, Number 3, June 1982, pages 653-669.
3. Werner Rheinboldt, John Burkardt,
   A Locally Parameterized Continuation Process,
   ACM Transactions on Mathematical Software,
   Volume 9, Number 2, June 1983, pages 215-235.
4. Werner Rheinboldt, John Burkardt,
   Algorithm 596: A Program for a Locally Parameterized Continuation Process,
   ACM Transactions on Mathematical Software,
   Volume 9, Number 2, June 1983, pages 236-241.
5. Werner Rheinboldt,
   Numerical Analysis of Parameterized Nonlinear Equations,
   Wiley, 1986,
   ISBN: 0-471-88814-1,
   LC: QA372.R54.
6. Werner Rheinboldt,
   Sample Problems for Continuation Processes,
   Technical Report ICMA-80-?,
   Institute for Computational Mathematics and Applications,
   Department of Mathematics,
   University of Pittsburgh, November 1980.
7. Werner Rheinboldt,
   Solution Fields of Nonlinear Equations and Continuation Methods,
   SIAM Journal on Numerical Analysis,
   Volume 17, Number 2, April 1980, pages 221-237.
8. Werner Rheinboldt,
   On the Solution of Some Nonlinear Equations Arising in the Application of Finite Element Methods,
   in The Mathematics of Finite Elements and Applications II,
   edited by John Whiteman,
   Academic Press, 1976,
   LC: TA347.F5.M37.

Data File Directories:

P01 is the Freudenstein-Roth function:

• p01_opt01, Problem 01, option 01, Freudenstein Roth;
• p01_opt04, Problem 01, option 04, Freudenstein Roth;

P06 is the Aircraft Stability function:

• p06_opt01, Problem 06, option 01, Aircraft Stability;
• p06_opt02, Problem 06, option 02, Aircraft Stability;
• p06_opt03, Problem 06, option 03, Aircraft Stability;
• p06_opt04, Problem 06, option 04, Aircraft Stability;
• p06_opt05, Problem 06, option 05, Aircraft Stability;

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