Numerical method

In numerical analysis, a numerical method is a mathematical tool designed to solve numerical problems. The implementation of a numerical method with an appropriate convergence check in a programming language is called a numerical algorithm.

Let ${\displaystyle F(x,y)=0}$ be a well-posed problem, i.e. ${\displaystyle F:X\times Y\rightarrow \mathbb {R} }$ is a real or complex functional relationship, defined on the cross-product of some input data set ${\displaystyle X}$ and an output set ${\displaystyle Y}$, such that exists a locally lipschitz function ${\displaystyle g:X\rightarrow Y}$ called resolvent, which has the property that for every root ${\displaystyle (x,y)}$ of ${\displaystyle F}$, ${\displaystyle y=g(x)}$. We define numerical method for the approximation of ${\displaystyle F(x,y)=0}$, the sequence of problems

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