E x i

Inserting in (8.4) and rearranging terms gives:

where

This equation, having the form x = f (x), can be conveniently solved using Wegstein's iterative procedure. For the reader's convenience, we give below the Algol-procedure as published by Wegstein (1958). The procedure computes a value of g = x satisfying the equation x = f (x). The calling statement gives the function, an initial approximation a = 0 to the root, and a tolerance parameter e for determining the number of significant figures in the solution.

procedure Root(f( ), a, epsilon)=(g) begin b=a ; c=f(b) ; g=c if (c=a) ; return d=a ; b=c ; e=c Hob: c=f(b)

g=(d(c-b(e)/(c-e-b+d) if(abs((g-b)/g)=<epsilon) ; return e=c ; d=b ; b=g ; go to Hob end m

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