Higher Education · Numerical Methods
Newton-Raphson
What is it
The Newton-Raphson method is an iterative technique for finding increasingly accurate approximations to the roots of an equation, using a function's value and gradient at a starting point to generate a better estimate at each step.
Why it matters
Newton-Raphson converges to a solution remarkably fast compared to simpler methods, making it the default root-finding technique used inside calculators, engineering software, and scientific computing whenever an equation can't be solved by an exact formula.
Exam tip
Always check the derivative isn't zero (or very close to zero) at your current estimate before applying the next iteration — a near-zero gradient causes the method to overshoot wildly or fail to converge entirely.
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