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Applications of multi-time methods to pattern recognition and other problems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 594)

Abstract

Systems of difference equations containing small parameters are studied by a constructive perturbation scheme analogous to the one developed by the authors for the study of differential equations. The method results in an averaging procedure for difference equations, and it is particularly well suited to certain highly oscillatory, nonlinear systems. The method is applied to problems from population genetics, pattern recognition, regression analysis, and the numerical analysis of stiff differential equations.

Keywords

  • Difference Equation
  • Recurrence Relation
  • Average Procedure
  • Slow Time
  • Training Algorithm

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This research was supported in part (F.C.H.) under Grant No. DAAG29-74-G-0219 by the U.S. Army Research Office.

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Bibliography

  1. F. C. Hoppensteadt, W. L. Miranker, Differential Equations Having Rapidly Changing Solutions, to appear in J. Differential Equations.

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© 1977 Springer-Verlag

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Hoppensteadt, F.C., Miranker, W.L. (1977). Applications of multi-time methods to pattern recognition and other problems. In: Brauner, CM., Gay, B., Mathieu, J. (eds) Singular Perturbations and Boundary Layer Theory. Lecture Notes in Mathematics, vol 594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086092

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  • DOI: https://doi.org/10.1007/BFb0086092

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08258-3

  • Online ISBN: 978-3-540-37340-7

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