Newton’s Method
Follow tangent-line root updates, inspect iterates and residuals, and compare convergence with horizontal tangents, repeated roots and cycles.
Free theory articleFollow tangent-line root updates, inspect iterates and residuals, and compare convergence with horizontal tangents, repeated roots and cycles.
Concept & interpretation
A root of a function satisfies f(x) = 0. Newton’s method replaces a curved graph near the current estimate with its tangent line, then uses the line’s x-intercept as the next estimate. The construction is easy to repeat, but a promising first step does not guarantee convergence. This module makes the estimates, function values and derivatives visible together.