Root-Finding Methods Explorer
Master numerical methods through interactive exploration
Root-finding methods are numerical algorithms that find values of x where a function f(x) equals zero. These "roots" or "zeros" are critical in engineering, physics, and mathematics for solving equations that can't be solved algebraically. Each method has different trade-offs between speed, reliability, and complexity.
Bisection and False Position methods trap the root between two points and systematically narrow the interval. They're reliable but can be slower.
Newton-Raphson and Secant methods use derivatives or slopes to rapidly converge. They're fast but require good initial guesses.
Fixed-Point iteration reformulates f(x)=0 as x=g(x) and iteratively refines the solution. Convergence depends on the choice of g(x).
Methods differ in how quickly they approach the root. Newton's method has quadratic convergence (error squares each iteration), while bisection has linear convergence (error halves each iteration).
Bracketing methods always converge if the initial interval contains a root, but open methods can diverge with poor initial guesses. Choose based on your problem's requirements.
Select a function below to see how different methods perform. Each example demonstrates unique convergence behaviors.
Enter your function and get intelligent suggestions for fixed-point iteration forms.
*The AI assistant provides mathematical rearrangements but may occasionally make errors.