False Position Method for Root Finding

🔍 About the False Position Method

The False Position Method (Regula Falsi) combines the reliability of the bisection method with the faster convergence of the secant method. It uses linear interpolation between two points that bracket the root.

c = a - f(a) × [(b - a) / (f(b) - f(a))]

Advantages: Always converges (like bisection), faster than bisection method, doesn't require derivative.

Requirements: Two points a and b where f(a) × f(b) < 0 (function changes sign).

Method Comparison:

Method	Convergence	Reliability	Requirements
Bisection	Linear (slow)	Always converges	f(a) × f(b) < 0
Secant	Superlinear (fast)	May diverge	Two initial guesses
False Position	Superlinear (fast)	Always converges	f(a) × f(b) < 0

Function f(x):

Left Endpoint (a):

Right Endpoint (b):

Tolerance (ε):

Supported Functions: Use x^2 for x², sin(x), cos(x), tan(x), ln(x), log(x), sqrt(x), exp(x), abs(x)
Examples: x^3 - x - 1, sin(x) - x/2, x^2 - 4, ln(x) - 1
Note: Ensure f(a) and f(b) have opposite signs for guaranteed convergence.

📊 False Position Method

🔍 About the False Position Method

Method Comparison:

False Position Method Results