Enter the function and initial values
Function and Secant Graph
Blue: function · Orange: secant line · Green: endpoints · Red: x-axis intersection.
Current iteration
Detailed calculation
Iteration Table
| n | aₙ | bₙ | f(aₙ) | f(bₙ) | xₙ₊₁ | f(xₙ₊₁) |
|---|---|---|---|---|---|---|
| No result | ||||||
How do the secant methods work?
In the false position method, start with a continuous function on [a₀,b₀] whose endpoint values have opposite signs. The secant through (aₙ,f(aₙ)) and (bₙ,f(bₙ)) intersects the x-axis at xₙ₊₁. False position retains the subinterval with opposite endpoint signs; the classical method instead updates both points.
The false position method (regula falsi) always preserves opposite signs at the endpoints. The classical secant method uses the two most recent approximations without requiring a sign change. The latter can converge faster near a root, but it can also diverge. Continuity and uniqueness cannot be established automatically for every expression. The simulator limits calculations to 200 iterations.
Worked example
Consider f(x) = x³ − x − 2 on [1, 2]. Since f(1) = −2 and f(2) = 4, the first secant intersects the x-axis at x₁ = 4/3 ≈ 1.333333. Repeating the procedure gives a root near 1.52138.
Use Next step and Previous step to follow the changing interval and each iteration.