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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Chui, Charles and Lai, Hang-Chin, “Vandermonde determinant and Lagrange interpolation in R3”, Lecture Notes in Pure and Applied Mathematics, 107 23–35, 1987.
Davis, P., Interpolation and Approximation, Blaisdell Publishing Company, New York, 1963.
Gelfond, A. O., Transcendental and Algebraic Numbers, Dover Publications, New York, 1960.
Martin, Clyde and Smith, Jennifer, “Approximation, Interpolation and Sampling”, Contemporary Mathematics, 68, 227–252, 1987.
Martin, C. F. and Wallace, D. I., “Observability and Transcendental Number Theory”, to appear.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Birkhäuser Boston
About this chapter
Cite this chapter
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
Download citation
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