Rayleigh–Ritz method

The Rayleigh–Ritz method allows for the computation of Ritz pairs ${\displaystyle ({\tilde {\lambda }}_{i},{\tilde {\textbf {x}}}_{i})}$ which approximate the solutions to the eigenvalue problem

Where ${\displaystyle A\in \mathbb {C} ^{N\times N}}$.

The procedure is as follows:

One can always compute the accuracy of such an approximation via ${\displaystyle \|A{\tilde {\textbf {x}}}_{i}-{\tilde {\lambda }}_{i}{\tilde {\textbf {x}}}_{i}\|}$

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