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Methods of Mathematical Physics, Third Edition by Bertha Jeffreys, Harold Jeffreys

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Chapter 9NUMERICAL METHODS

I have no satisfaction in formulas unless I feel their numerical magnitude.

LORD KELVIN, Life by Sylvanua Thompson, p. 827

9·01. Approximation by polynomials.

The characteristic feature of most numerical methods is that values of a function f(x) are given for a set of distinct values of x, but not for intermediate values; for purposes of computation these are filled in on the hypothesis that f(x) can be replaced by a polynomial agreeing with f(x) at the places where its values are given. The simplest case is that of linear interpolation, in which only two adjacent values of f(x) are taken from a table and intermediate values are calculated on the supposition that f′(x) is constant in the interval. This procedure is ...

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