ニュートン法での零点を近似する。
(define dx 0.00001) (define (deriv g) (lambda (x) (/ (- (g (+ x dx)) (g x)) dx))) (define (newton-transform g) (lambda (x) (- x (/ (g x) ((deriv g) x))))) (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 (newtons-method g guess) (fixed-point (newton-transform g) guess)) (define (cube x) (* x x x)) (define (square x) (* x x)) (define (cubic a b c) (lambda (x) (+ (cube x) (* a (square x)) (* b x) c)))
答えが簡単にわかるので、の零点を計算します!
gosh> (newtons-method (cubic 0 0 8) 1) -1.999999999999997