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Interpolating Uniquely with Only a Finite Class of Polynomials

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Robust Control of Linear Systems and Nonlinear Control

Part of the book series: Progress in Systems and Control Theory ((PSCT,volume 4))

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Abstract

This paper draws from theorems in transcendental number theory to answer questions about interpolation with a finite class of multivariable polynomials. In particular we describe sets of data points at which a unique polynomial from a particular class gives us a good approximation of the output.

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References

  1. Chui, Charles and Lai, Hang-Chin, “Vandermonde determinant and Lagrange interpolation in R3”, Lecture Notes in Pure and Applied Mathematics, 107 23–35, 1987.

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  3. Gelfond, A. O., Transcendental and Algebraic Numbers, Dover Publications, New York, 1960.

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  4. Martin, Clyde and Smith, Jennifer, “Approximation, Interpolation and Sampling”, Contemporary Mathematics, 68, 227–252, 1987.

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  5. Martin, C. F. and Wallace, D. I., “Observability and Transcendental Number Theory”, to appear.

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© 1990 Birkhäuser Boston

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DeStefano, A., Kostelec, P., Wallace, D.I. (1990). Interpolating Uniquely with Only a Finite Class of Polynomials. In: Kaashoek, M.A., van Schuppen, J.H., Ran, A.C.M. (eds) Robust Control of Linear Systems and Nonlinear Control. Progress in Systems and Control Theory, vol 4. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4484-4_49

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  • DOI: https://doi.org/10.1007/978-1-4612-4484-4_49

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8839-8

  • Online ISBN: 978-1-4612-4484-4

  • eBook Packages: Springer Book Archive

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