Definition:Ritz Method

Definition
Let $\mathcal M$ be a normed linear space.

Let $J\sqbrk y$ be a functional defined on space $\mathcal M$.

Let $\sequence{\phi_n}$ be an infinite sequence of mappings in $\mathcal M$.

Let $\mathcal M_n$ be an $n$-dimensional linear subspace of $\mathcal M$, spanned by first $n$ mapping of $\sequence{\phi_n}$.

Let $\eta_n=\boldsymbol\alpha\boldsymbol\phi$, where $\boldsymbol\alpha$ is a real $n$-dimensional vector.

Minimise $J\sqbrk{\eta_n}$ $\boldsymbol\alpha$.

Then $J\sqbrk{\eta_n}$ is an approximate minimum of $J\sqbrk y$, and is denoted by $\mu_n$.

This method is known as Ritz method.

Also see

 * Definition:Ritz Sequence