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Numerical Analysis
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
The inverse iteration method applies the power method idea to A−1 to compute λn−1 and the associated eigenvector vn. The algorithm does not require computing
Iterative Methods
Published in Jeffery J. Leader, Numerical Analysis and Scientific Computation, 2022
Inverse iteration is a good technique for improving the accuracy of an eigenvalue or eigenvector, for finding an eigenvector corresponding to a known eigenvalue, or for finding a single eigenvalue near a given value σ. If more than just a few eigenpairs of A are sought, however, there are significantly more efficient methods.
Convergence analysis of iterative learning control using pseudospectra
Published in International Journal of Control, 2022
Zahra Shahriari, Bo Bernhardsson, Olof Troeng
This algorithm can be made more efficient by computing only the smallest singular value, rather than the entire singular values. One way to accomplish this is through inverse iteration method. Let . Since the problem is reduced to finding the smallest eigenvalue of , which is equal to the largest eigenvalue of . The inverse iteration algorithm uses the power method on and its convergence rate is given by the smallest two singular values of B. This method involves LU factorisation of B, which is a major bottleneck in computation. For every point z on the grid, the factorisation of requires operations. Therefore, on the full grid of points, this procedure has the complexity of , which is the same complexity as calculating the entire set of singular values.
3D mixed finite elements for curved, flat piezoelectric structures
Published in International Journal of Smart and Nano Materials, 2019
Martin Meindlhumer, Astrid Pechstein
A wide range of technical applications involving piezoelectric structures is operated in the regime of (mechanical) vibrations e.g. noise and vibration control and damping, shape control or energy harvesting. To design and study these applications the computation of their eigenfrequencies and -forms may be required. The finite element discretization leads to a system with a huge number of eigenvalues of which typically only a few of the smallest are of interest. In our contribution we propose to use the inverse iteration procedure which allows the effective computation of a certain number of eigenvalues.