Secant method: xₙ₊₁ = xₙ − f(xₙ)(xₙ−xₙ₋₁)/(f(xₙ)−f(xₙ₋₁)). Like Newton's method but replaces f' with a secant line approximation. Convergence order ≈ 1.618 (golden ratio). No derivative needed, but requires two initial points.
How to Use
Set up the problem:
- f(x): Choose function
- x₀, x₁: Two initial guesses
- Output: Root + iterations
vs. Newton's
- Newton: needs f', O(h²) per step
- Secant: no f', O(h^1.618) per step
- Bisection: always converges, O(h) per step
Convergence
Superlinear: order φ ≈ 1.618. Faster than bisection but slower than Newton. May fail if secant is nearly horizontal (f(xₙ)≈f(xₙ₋₁)).
Step-by-Step Instructions
- 1Select a function.
- 2Enter x₀ and x₁.
- 3View iterations.
- 4Track convergence.
- 5Get root.