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Newton-Raphson Method

★★★☆☆High School

📖Definition

Newton-Raphson method is an iterative technique for finding roots of f(x) = 0. It uses tangent lines for fast convergence.

x_n+1 = xₙ - (f(xₙ))/(f'(xₙ))

Newton-Raphson iteration formula

예제 1

Find √2 using Newton's method (f(x) = x² - 2, x₀ = 1).

Discovered by: Isaac Newton, Joseph Raphson (17th century)

Newton developed it for polynomial roots; Raphson generalized it.

Nonlinear equation solving

Newton optimization

Ray tracing

#뉴턴#근찾기#Newton#root finding