TENSOLVE

Nonlinear equations and nonlinear least squares

This package find roots of systems of n nonlinear equations in n unknowns, or minimizers of the sum of squares of m>n nonlinear equations in n unknowns. It allows the user to choose between a tensor method based on a quadratic model and a standard method based on a linear model. Both models calculate an analytic or finite difference Jacobian matrix at each iteration. The tensor method augments the linear model with a low-rank, second-order term that is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Either a line search or trust region step selection strategy may be selected. The tensor method is significantly more efficient than the standard method in iterations, function evaluations, and time. It is especially useful on problems where the Jacobian matrix at the solution is singular.

The software can be called with an interface where the user supplies only the function, number of variables, and starting point; default choices are made for all other input parameters. An alternative interface allows the user to specify any input parameters that are different from the defaults.

The software is written in Fortran 77 using double precision. The only machine dependency is upon machine epsilon, which is either calculated by the software or provided by the user.

Need more info?

Contact:

Robert B. Schnabel 
Department of Computer Science 
University of Colorado 
Boulder, CO 80309-0430 
Phone: (303) 492-7554 
bobby@cs.colorado.edu

References:

R. B. Schnabel and P. Frank, Tensor methods for nonlinear equations, SIAM J. Numer. Anal. 21 (1984), pp. 814--843.

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