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Title: TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods

Abstract

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.

Authors:
 [1];  [2]
  1. Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
  2. Colorado Univ., Boulder, CO (United States). Dept. of Computer Science
Publication Date:
Research Org.:
Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
Sponsoring Org.:
USDOE Office of Energy Research, Washington, DC (United States); Department of Defense, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
OSTI Identifier:
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
DOE Contract Number:  
W-31109-ENG-38
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: [1996]
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; TENSORS; T CODES; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; OPTIMIZATION; LEAST SQUARE FIT; MATRICES; ITERATIVE METHODS; JACOBIAN FUNCTION

Citation Formats

Bouaricha, A, and Schnabel, R B. TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods. United States: N. p., 1996. Web. doi:10.2172/435303.
Bouaricha, A, & Schnabel, R B. TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods. United States. https://doi.org/10.2172/435303
Bouaricha, A, and Schnabel, R B. 1996. "TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods". United States. https://doi.org/10.2172/435303. https://www.osti.gov/servlets/purl/435303.
@article{osti_435303,
title = {TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods},
author = {Bouaricha, A and Schnabel, R B},
abstractNote = {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.},
doi = {10.2172/435303},
url = {https://www.osti.gov/biblio/435303}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Dec 31 00:00:00 EST 1996},
month = {Tue Dec 31 00:00:00 EST 1996}
}