🧮 Numerical Methods

Root Finding Calculator Suite

Interactive implementations of classical numerical methods

Welcome to the Numerical Methods Calculator

Explore and compare different root-finding algorithms with our interactive calculators. Each method provides detailed step-by-step iterations, convergence analysis, and professional visualizations to help you understand how these fundamental numerical techniques work.

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Try searching for: "bisection", "newton", "secant", "false position", or "fixed point"

Bisection Method

Bracketing Method
A reliable root-finding algorithm that repeatedly bisects an interval and selects the subinterval where the function changes sign.
  • Always converges when f(a)×f(b) < 0
  • Linear convergence rate
  • Simple and robust implementation
  • Requires interval with sign change
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Secant Method

Open Method
An iterative method that uses linear interpolation between two points to approximate the derivative and find roots faster.
  • Superlinear convergence rate
  • No derivative calculation needed
  • Faster than bisection method
  • May diverge with poor initial guesses
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False Position Method

Hybrid Method
Combines the reliability of bisection with the speed of secant method using linear interpolation between bracketing points.
  • Always converges like bisection
  • Faster convergence than bisection
  • Uses linear interpolation
  • Best of both worlds approach
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Newton-Raphson Method

Open Method
A powerful iterative method using derivatives to achieve quadratic convergence, making it one of the fastest root-finding algorithms.
  • Quadratic convergence rate (very fast)
  • Requires function derivative
  • Sensitive to initial guess
  • Best performance when it converges
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Fixed Point Method

Successive Approximation
An iterative method that finds roots by rearranging f(x) = 0 to x = g(x), then using successive approximations.
  • Simple iteration: xi+1 = g(xi)
  • Convergence depends on |g'(x)| < 1
  • Easy to understand and implement
  • Requires careful choice of g(x)
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Birge Vieta Method

Polynomial Method
A specialized method for finding roots of polynomial equations using synthetic division and Newton-Raphson iteration.
  • Efficient for polynomial equations
  • Uses synthetic division technique
  • Combines Horner's method with Newton-Raphson
  • Ideal for polynomial root finding
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Method Comparison

Method Convergence Rate Reliability Initial Requirements Best Use Case
Bisection Linear (slow) Always converges f(a) × f(b) < 0 When reliability is crucial
Secant Superlinear (fast) May diverge Two good initial guesses When speed is important
False Position Superlinear (fast) Always converges f(a) × f(b) < 0 Best balance of speed & reliability
Newton-Raphson Quadratic (very fast) May diverge Good initial guess + f'(x) When derivative is available & speed is critical
Fixed Point Linear (depends on g'(x)) Depends on g(x) choice Good initial guess + |g'(x)| < 1 When equation can be rearranged to x = g(x)
Birge Vieta Quadratic (very fast) Reliable for polynomials Polynomial coefficients + initial guess When solving polynomial equations efficiently

Numerical Methods Calculator Suite

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