## 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 ...