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On uniqueness conditions for optimal curve fitting


We show that the standard uniqueness condition for an important class of optimal curve-fitting problems is equivalent to an observability condition on an associated dynamical model. This fact allows uniqueness to be checked by testing the rank of a matrix.

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  1. 1.

    Greville, T. N. E., Editor,Theory and Applications of Spline Functions, Academic Press, New York, New York, 1969.

  2. 2.

    Weinert, H. L., andKailath, T.,Stochastic Interpretations and Recursive Algorithms for Spline Functions, Annals of Statistics, Vol. 2, pp. 787–794, 1974.

  3. 3.

    Weinert, H. L., andSidhu, G. S.,A Stochastic Framework for Recursive Computation of Spline Functions, Part I: Interpolating Splines, IEEE Transactions on Information Theory, Vol. IT-24, No. 1, 1978.

  4. 4.

    Jerome, J., andSchumaker, L. L.,On Lg-Splines, Journal of Approximation Theory, Vol. 2, pp. 29–49, 1969.

  5. 5.

    Gilchrist, J. D.,n-Observability for Linear Systems, IEEE Transactions on Automatic Control, Vol. AC-11, pp. 388–395, 1966.

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Communicated by D. G. Luenberger

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Weinert, H.L., Sidhu, G.S. On uniqueness conditions for optimal curve fitting. J Optim Theory Appl 23, 211–216 (1977).

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Key Words

  • Spline interpolation
  • observability
  • curve fitting
  • linear systems