 Ritz method

The Ritz method minimizes a quadratic energy over a finite-dimensional trial space. For basis functions ${\varphi }_j$ and bilinear form $a$, its linear system is $Ka=F$ with $K_{jk}=a({\varphi }_k,{\varphi }_j)$ and $F_j=⟨f,{\varphi }_j⟩$.

The Ritz method is a variational technique used in mathematical analysis, particularly in the fields of applied mathematics and engineering, to find approximate solutions to complex problems, typically involving differential equations. It is particularly useful for problems in structural mechanics, quantum mechanics, and other fields where the governing equations can be difficult to solve exactly.