Let X, Y, and Z be real separable Hilbert spaces, let T : X → Y be a compact operator, and let L : D(L) → Z be a closed and densely defined linear operator. Then the generalized singular value expansion (GSVE) is an expansion that expresses T and L in terms of a common orthonormal basis. Under certain hypotheses on discretization, the GSVE of an approximate operator pair (Tj, Lj), where Tj : Xj → Yj and Lj : Xj → Zj, converges to the GSVE of (T, L). Error estimates establish a rate of convergence that is consistent with numerical experiments in the case of discretization using piecewise linear finite elements. Further numerical testing suggests that a higher rate of convergence is attained by using higher order elements. However, the theory does not cover this case.
|Advisor:||Gockenbach, Mark S.|
|Commitee:||Masoud, Hassan, Ong, Benjamin W., Sun, Jiguang|
|School:||Michigan Technological University|
|School Location:||United States -- Michigan|
|Source:||DAI-B 80/09(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Mathematics|
|Keywords:||Generalized singular value expansion|
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