Particle Spreading in a Simple Majda Flow and Eigenvalue Estimation Through a Cayley Transform
Lee, Jae-Ug
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https://hdl.handle.net/2142/86876
Description
Title
Particle Spreading in a Simple Majda Flow and Eigenvalue Estimation Through a Cayley Transform
Author(s)
Lee, Jae-Ug
Issue Date
2006
Doctoral Committee Chair(s)
Bronski, Jared C.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
The spectrum of the integral operator whose kernel is the covariance function of a random variable plays an important role in finding the distribution of the random variable. We consider methods for producing estimates of the eigenvalues of such operators. If such an operator can be written in the form H0 + H1 with H 1 relatively compact to H0, then the eigenvalues are asymptotically close to those of H0. This method does not, however, produce good error estimates. We consider a perturbation method based on a Cayley transform. We show that the change of basis V = (I + K/2)-1( I - K/2), where I is the identity operator and K is a skew-adjoint operator given by a formal perturbation argument, gives better error estimate.
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