🖥️

Bisection Method

★★☆☆☆Middle School

📖Definition

Bisection method is the simplest root-finding method for continuous functions. It halves the interval, narrowing toward sign changes.

c = (a + b)/(2)

Midpoint calculation

if f(a)f(c) < 0: b = c, else a = c

Interval update rule

|xₙ - r| ≤ (b-a)/(2^n+1)

Error bound after n iterations

예제 1

Find root of f(x) = x² - 2 in [1, 2] using bisection.

Safe root finding

Mathematical basis of binary search

Break-even calculation

#이분법#근찾기#bisection#root finding