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Consider the function f(x) = log(1 + x), assume that the interpolating polynomial P(x) is used with interpolation nodes at xi = 1, 3, 5,
Consider the function f(x) = log(1 + x), assume that the interpolating polynomial P(x) is used with interpolation nodes at xi = 1, 3, 5, 7, 9. Find an upper bound for the interpolation error at x = 0.
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In order to get the upper bound of the interpolation error at 0 x 0 We can apply the error bound formula for interpolating polynomials with the interpolating polynomial Px We can utilize the error bound formula using Lagrange interpolation since the function log fxlog1x is continuous on the interval 1 9 and has continuous derivatives up to the fourth derivative on this interval For Lagrange interpolation the error bound is provided by 1 0 1 fxPx n1 M The function xx 0 xx 1 xx n where M is an upper bound for ...
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Precalculus
Authors: Jay Abramson
1st Edition
1938168348, 978-1938168345
