SICP 1.3.4 牛顿法

(define (deriv g)
(lambda (x)
(/ (- (g (+ x dx)) (g x))
dx)))

(define dx 0.00001)

(define (newton-transform g)
(lambda (x)
(- x (/ (g x) ((deriv g) x)))))

(define (newtons-method g guess)
(fixed-point (newton-transform g) guess))

(define tolerance 0.00001)

(define (fixed-point f first-guess)
(define (close-enough? v1 v2)
(< (abs (- v1 v2)) tolerance))
(define (try guess)
(let ((next (f guess)))
(if (close-enough? guess next)
next
(try next))))
(try first-guess))

(define (sqrt-a x)
(newtons-method (lambda (y) (- (square y) x)) 1.0))

(sqrt-a 2.0)