The Approximation of Certain Functions by Compound Means

Abstract

We begin with the double recurrence relation

$$ u_{n + 1} = \frac{1} {2}(u_n + v_n ), $$

(1a)

$$ v_{n + 1} = (u_{n + 1} v_n )^{1/2} , $$

(1b)

where u₀, v₀ are given. We will refer to (1) as the Schwab-Borchardt algorithm following Schoenberg [10, 11], who has made a careful study of its origins. Hitherto this process has been more commonly identified in the literature solely with the name of Borchardt. (See, for example, Carlson [2], Todd [13].)

Paper presented by this author.