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10 cards from this deck
Simultaneous equations: y=xy = xy=x and y=g(x)y = g(x)y=g(x)
Choose initial x0x_0x0, find yyy on y=g(x)y = g(x)y=g(x) curve
Move to y=xy = xy=x line, use this as new xxx-value
When suitably close to root (if converges)
Root exists in the interval
One side of equation = 0 and function continuous
xn+1=g(xn)x_{n+1} = g(x_n)xn+1=g(xn)
x=3−x34x = \frac{3 - x^3}{4}x=43−x3
x=ln(x+3)ln3x = \frac{\ln(x + 3)}{\ln 3}x=ln3ln(x+3)
How iteration converges visually
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