TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods
- Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
- Colorado Univ., Boulder, CO (United States). Dept. of Computer Science
This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.
- Research Organization:
- Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States); Department of Defense, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 435303
- Report Number(s):
- MCS-P-463-0894; ON: DE97002613; CNN: AFOSR Grant AFOSR-90-0109; AFOSR Grant F49620-94-1-0101; ARO Grant DAAL03-91-G-0151; ARO Grant DAA H04-94-G-0228; NSF Grant CCR-9101795
- Resource Relation:
- Other Information: PBD: [1996]
- Country of Publication:
- United States
- Language:
- English
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