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Newton-Raphson Method

ÀÛ¼ºÀÚ Uploader : today ÀÛ¼ºÀÏ Upload Date: 2019-09-02º¯°æÀÏ Update Date: 2019-10-05Á¶È¸¼ö View : 320

Numerical method to solve the differentiable function f(x). It finds the equation of tangent line tangent to f(x) at arbitrary x1 and its intercept x2 at x-axis, then finds the equation of tangent line tangent to f(x) at x2 and its intercept at x-axis. By Repeating this way, the solution of f(x) can be obtained. (Refer the figure.)

f(x): Differentiable function
f¡Ç(x): Differential function of f(x)
y: equation of tangent line

Since y = f¡Ç(x1)x+b,

y1 = f¡Ç(x1)x1+b
b = y1 - f¡Ç(x1)x1

Thus, the tangent line y is :
y = f¡Ç(x1)x + y1 - f¡Ç(x1)x1

Since y=0 at the intercept by the x-axis,

f¡Ç(x1)x2 = f¡Ç(x1)x1 - y1
x2 = x1 - y1/f¡Ç(x)

From y1 = f(x1),

x2 = x1 - f(x1)/f¡Ç(x1)  

Note that f(x1) is expressed as fx1 and the derivative of f(x1) as gx1.

*** Âü°í¹®Çå[References] ***

x2 = x1 - fx1 / gx1
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