An overview of Ritz and Eigen vectors, taken from the CSI Analysis Reference Manual (Modal Analysis > Overview, page 323), is given as follows:


Eigen modes are most suitable for determining response from horizontal ground acceleration, though a missing-mass (residual-mass) mode may need to be included to account for missing high-frequency effects. Mass participation is a common measure for determining whether or not there are enough modes, though it does not provide information about localized response.

Eigen analysis is useful for checking behavior and locating problems within the model. Another benefit is that natural frequencies indicate when resonance should be expected under different loading conditions. Users may control the convergence tolerance. Orthogonality is strictly maintained to within the accuracy of the machine (15 decimal digits). Sturm sequence checks are performed and reported to avoid missing Eigen vectors when using shifts. Internal accuracy checks are performed and used to automatically control the solution. Ill-conditioned systems are detected and reported, then still produce Eigen vectors which may be used to trace the source of the modeling problem.

Ritz vectors

Load-dependent Ritz vectors are most suitable for analyses involving vertical ground acceleration, localized machine vibration, and the nonlinear FNA method. Ritz vectors are also efficient and widely used for dynamic analyses involving horizontal ground motion. Their benefit here is that, for the same number of modes, Ritz vectors provide a better participation factor, which enables the analysis to run faster, with the same level of accuracy.

Further, missing-mass modes are automatically included, there is no need to determine whether or not there are enough modes, and when determining convergence of localized response with respect to the number of modes, Ritz vectors converge much faster and more uniformly than do Eigen vectors. Ritz vectors are not subject to convergence questions, though strict orthogonality of vectors is maintained, similar to Eigen vectors.

Sources of documentation on Load-dependent Ritz vectors include: