Power methods for calculating eigenvalues and eigenvectors of spectral operators on Hilbert spaces

Power, inverse power and orthogonal iteration algorithms for determining the eigenstructure of operators on infinite-dimensional Hilbert spaces are developed. Convergence properties of the algorithms are established for certain classes of operators associated with the control of systems described by partial differential equations. A simple finite-difference method is applied to a particular operator to illustrate the utility of the algorithms.

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