7 Polynomial and piecewise polynomial interpolation

  • Published 2008

Abstract

Let f be a function, which is only known at the nodes x1, x2, . . . , xn, i.e., all we know about the function f are its values yj = f(xj), j = 1, 2, . . . , n. For instance, we may have obtained these values through measurements and now would like to determine f(x) for other values of x. Example 7.1: Assume that we need to evaluate cos(π/6), but the trigonometric function-key on your calculator is broken and we do not have access to a computer. We do remember that cos(0) = 1, cos(π/4) = 1/ √ 2, and cos(π/2) = 0. How can we use this information about the cosine function to determine an approximation of cos(π/6)? 2 Example 7.2: Let x represent time (in hours) and f(x) be the amount of rain falling at time x. Assume that f(x) is measured once an hour at a weather station. We would like to determine the total amount of rain fallen during a 24-hour period, i.e., we would like to compute

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Cite this paper

@inproceedings{20087PA, title={7 Polynomial and piecewise polynomial interpolation}, author={}, year={2008} }