Newton's method [SEP] named after
Newton's method
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function defined for a real variable , the function's derivative , and an initial guess for a root of . If the function satisfies sufficient assumptions and the initial guess is close, then
Steffensen's method
In numerical analysis, Steffensen's method is a root-finding technique similar to Newton's method, named after Johan Frederik Steffensen. Steffensen's method also achieves quadratic convergence, but without using derivatives as Newton's method does.
Simple description.
The simplest form of the formula for Steffensen's method occurs when it is used to find the zeros, or roots, of a function formula_1 ; that is: to find the value formula_2 that satisfies formula_3 . Near the solution formula_2 ,