# Definition:Ritz Method

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## Contents

## 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 $J\sqbrk{\eta_n}$ with respect to $\boldsymbol\alpha$.

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

## Source of Name

This entry was named for Walther Ritz.

## Sources

- 1963: I.M. Gelfand and S.V. Fomin:
*Calculus of Variations*... (previous) ... (next): $\S 8.40 $: The Ritz Method and the Method of Finite Differences