SWAC Experiments on the Use of Orthogonal Polynomials for Data Fitting

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Abstract
I~l where q, is a polynomial of degree n, is minimized by q,~(x) = f~)(x). In [3] one of us discussed the problem of finding f~)(x) oh a digital computer and outlined certain advantages of determining f~)(x) in terms of polynomials pk(x) orthogonal over ~. It was further proposed that the pk(x) be computed from their 3-term recurrence. The procedure will be outlined again here, mainly to formulate our notation. Let po(x) = 1, and let/~0 = 0. Then the polynomials pk(x) are defined and computed by the recurrence

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