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- (declare (usual-integrations))
- (define (false-position-search f x1 x2 epsilon)
- (define (fpsl x1 fx1 x2 fx2)
- (let ((afx1 (abs fx1)) (afx2 (abs fx2)))
- (define (best-guess)
- (if (opposite-sign? fx1 fx2)
- (average x1 x2)
- (if (< afx1 afx2) x1 x2)))
- (if (< afx1 epsilon)
- (if (< afx2 epsilon)
- (best-guess)
- x1)
- (if (< afx2 epsilon)
- x2
- (if (close-enuf? x1 x2 epsilon)
- (best-guess)
- (let* ((x (/ (- (* x2 fx1) (* fx2 x1))
- (- fx1 fx2)))
- (fx (f x)))
- (if (opposite-sign? fx1 fx)
- (fpsl x1 fx1 x fx)
- (fpsl x fx x2 fx2))))))))
- (fpsl x1 (f x1) x2 (f x2)))
- (define (newton-with-false-position-search f&df x1 x2 epsilon)
- (define (fpsl x1 fx1 dfx1 x2 fx2 dfx2)
- (define (try x)
- (if (opposite-sign? (- x x1) (- x x2))
- (begin
- (next x))
- (begin
- (next (/ (- (* x2 fx1) (* fx2 x1)) (- fx1 fx2))))))
- (define (next x)
- (f&df x
- (lambda (fx dfx)
- (if (opposite-sign? fx1 fx)
- (fpsl x1 fx1 dfx1 x fx dfx)
- (fpsl x fx dfx x2 fx2 dfx2)))))
- (let ((afx1 (abs fx1)) (afx2 (abs fx2)))
- (define (best-guess)
- (if (opposite-sign? fx1 fx2)
- (average x1 x2)
- (if (< afx1 afx2) x1 x2)))
- (if (< afx1 epsilon)
- (if (< afx2 epsilon)
- (best-guess)
- x1)
- (if (< afx2 epsilon)
- x2
- (if (close-enuf? x1 x2 epsilon)
- (best-guess)
- (if (< afx1 afx2)
- (try (- x1 (/ fx1 dfx1)))
- (try (- x2 (/ fx2 dfx2)))))))))
- (f&df x1
- (lambda (fx1 dfx1)
- (f&df x2
- (lambda (fx2 dfx2)
- (fpsl x1 fx1 dfx1 x2 fx2 dfx2))))))
- (define (average x y)
- (/ (+ x y) 2.0))
- (define (opposite-sign? x y)
- (< (* x y) 0.0))
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