Type of Document Dissertation Author Lee, Gyou-Bong URN etd-10142005-135800 Title A study of the computation and convergence behavior of eigenvalue bounds for self-adjoint operators Degree PhD Department Mathematics Advisory Committee
Advisor Name Title No Advisors Found Keywords
- Eigenvalues Research
- Convergence Research
Date of Defense 1991-05-05 Availability restricted Abstract
The convergence rates for the method of Weinstein and a variant method of Aronszajn known as "truncation including the remainder" are derived in terms of the containment gaps between exact and approximating subspaces, using analytical techniques that arise in part in the convergence analysis of finite element methods for differential eigenvalue problems. An example of a one dimensional Schrodinger operator with a potential is presented which arises in quantum mechanics.
Examples using the recent eigenvector-free (EVF) method of Beattie and Goerisch are considered. Since the EVF method uses finite element trial functions as approximating vectors, it produces sparse and well-structured coefficient matrices. For these large-order sparse matrix eigenvalue problems, we adapt a spectral transformation Lanczos algorithm for finding a few wanted eigenvalues. For a few particular examples of vibration in beams and plates, convergence behavior is experimentally evaluated.
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