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A parallel projection method for overdetermined nonlinear systems of equations

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Abstract

We consider overdetermined nonlinear systems of equationsF(x)=0, whereF: ℝn → ℝm,m≥n. For this type of systems we define “weighted least square distance” (WLSD) solutions, which represent an alternative to classical least squares solutions and to other solutions based on residual normas. We introduce a generalization of the classical method of Cimmino for linear systems and we prove local convergence results. We introduce a practical strategy for improving the global convergence properties of the method. Finally, numerical experiments are presented.

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Authors and Affiliations

  1. Department of Applied Mathematics, IMECC-UNICAMP, State University of Campinas, CP 6065, 13081, Campinas, SP, Brazil

    Maria A. Diniz-Ehrhardt & José Mario Martínez

Authors
  1. Maria A. Diniz-Ehrhardt
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  2. José Mario Martínez
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Additional information

Communicated by C. Brezinski

Work supported by FAPESP (Grant 90/3724/6), FINEP, CNPq and FAEP-UNICAMP.

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Diniz-Ehrhardt, M.A., Mario Martínez, J. A parallel projection method for overdetermined nonlinear systems of equations. Numer Algor 4, 241–262 (1993). https://doi.org/10.1007/BF02144106

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  • DOI: https://doi.org/10.1007/BF02144106

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