SICP Exercise 1.36
Modified fixed-point procedure:
(define (fixed-point f first-guess) (define (close-enough? v1 v2) (display "x=") (display v1) (display " and f(x)=") (display v2) (newline) (< (abs (- v1 v2)) tolerance)) (define (try guess) (let ((next (f guess))) (if (close-enough? guess next) next (try next)))) (try first-guess))
Without average damping:
> (fixed-point (lambda (x) (/ (log 1000) (log x))) 1.1)
This gives us the answer in 33 iterations.
With average damping:
> (fixed-point (lambda (x) (average x (/ (log y) (log x)))) 10.0)
This gives the answer in 10 iterations.