Polynomial algebra for Birkhoff interpolants |
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| Authors: | John C Butcher Robert M Corless Laureano Gonzalez-Vega Azar Shakoori |
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| Institution: | 1.Department of Mathematics,University of Auckland,Auckland,New Zealand;2.Department of Applied Mathematics,University of Western Ontario,London,Canada;3.Departamento de Matematicas, Estadistica y Computacion,Universidad de Cantabria,Santander,Spain |
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| Abstract: | We introduce a unifying formulation of a number of related problems which can all be solved using a contour integral formula.
Each of these problems requires finding a non-trivial linear combination of possibly some of the values of a function f, and possibly some of its derivatives, at a number of data points. This linear combination is required to have zero value
when f is a polynomial of up to a specific degree p. Examples of this type of problem include Lagrange, Hermite and Hermite–Birkhoff interpolation; fixed-denominator rational
interpolation; and various numerical quadrature and differentiation formulae. Other applications include the estimation of
missing data and root-finding. |
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