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

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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 ... continued below

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34 p.

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Bouaricha, A. & Schnabel, R. B. December 1996.

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This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 58 times , with 4 in the last month . More information about this report can be viewed below.

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  • Bouaricha, A. Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
  • Schnabel, R. B. Colorado Univ., Boulder, CO (United States). Dept. of Computer Science

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Description

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.

Physical Description

34 p.

Notes

OSTI as DE97002613

Source

  • Other Information: PBD: [1996]

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  • Other: DE97002613
  • Report No.: MCS-P--463-0894
  • Grant Number: W-31109-ENG-38
  • DOI: 10.2172/435303 | External Link
  • Office of Scientific & Technical Information Report Number: 435303
  • Archival Resource Key: ark:/67531/metadc680843

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Office of Scientific & Technical Information Technical Reports

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  • December 1996

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  • July 25, 2015, 2:20 a.m.

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  • Dec. 11, 2015, 3:04 p.m.

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Bouaricha, A. & Schnabel, R. B. TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods, report, December 1996; Illinois. (digital.library.unt.edu/ark:/67531/metadc680843/: accessed December 16, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.