Bisection method: if f(a)·f(b)<0, root exists in [a,b]. Midpoint c=(a+b)/2. If f(a)·f(c)<0, root in [a,c]; else root in [c,b]. Repeat. Error ≤ (b−a)/2ⁿ after n iterations. Always converges (unlike Newton/secant).
How to Use
Set up the bracket:
- f(x): Choose function
- [a, b]: Bracket with sign change
- Tolerance: Desired accuracy
Why It Always Works
By the Intermediate Value Theorem, if f is continuous and f(a)·f(b)<0, there's a root in [a,b]. Each iteration halves the interval. After n steps, error ≤ (b−a)/2ⁿ.
Trade-offs
- Pro: Always converges
- Pro: Simple to implement
- Con: Linear convergence (slow)
- Con: Need initial bracket
Step-by-Step Instructions
- 1Select a function.
- 2Enter bracket [a,b].
- 3Set tolerance.
- 4View iterations.
- 5Get root.