On axially symmetric flow and the method of generalized electrostatics
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Scarborough, 2nd edition, pp. 99-103, the mistake arising from identification of two ^-values in the interval which may be distinct.) Consider the given data / (J) — j for j = 0, 1, • • • , n, for which the polynomial approximation is p(x) = x. Can the error be bounded by any function of x0 , • • • , xn , y0 = f(x0), • • • , y„ = f (xn) ? That it cannot is clear from the function f(x) = x + k sin ttx. We have /(J) = f + k, p(§) = §, and /(J) — p(|) = k. Since k is independent of x,and /(x,), this error value cannot be bounded by any function of these without strong hypotheses on the function /
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