scheme牛顿迭代

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  • 求平方根
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(define (square x) (* x x))

(square 2)

(define (abs x)
  (if (< x 0) (- x) x)
  )

(abs -1)

;;(define (goodenough guess x)
;;  (< (abs (- (square guess) x)) 0.0001))

(define (goodenough guess x)
  (< (abs (- (/ guess (average guess (/ x guess))) 1)) 0.01))

(goodenough 3 9)

(define (average a b)
  (/ (+ a b) 2))

(average 9 3)

(define (sqrt-iter guess x)
  (if (goodenough guess x) guess (sqrt-iter (average guess (/ x guess)) x))
  )

(sqrt-iter 1.0 9)

(define (sqrt x) (sqrt-iter 1.0 x))

(sqrt 9)
  • 求立方根
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(define (square x) (* x x))

(square 2)

(define (cube x) (* x x x))

(cubert 2)

(define (abs x)
  (if (< x 0) (- x) x)
  )

(abs -1)
(abs 1)

(define (goodenough guess x)
  (< (abs (- (/ guess (improve guess x)) 1)) 0.01))

(goodenough 3 9)

(define (improve guess x)
  (/ (+ (/ x (square guess)) (* 2 guess)) 3))

(improve 1.0 9)

(define (average a b)
  (/ (+ a b) 2))

(average 9 3)

(define (cubert-iter guess x)
  (if (goodenough guess x) guess (cubert-iter (improve guess x) x))
  )

(cubert-iter 2.0 27)

(define (cubert x) (cubert-iter 1.0 x))

(cubert 27)

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