2026-09-18T19:09:03Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1590912026-08-04T08:52:27Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Urschel, John
Chen, Cecilia
2025-04-14T14:05:02Z
2025-04-14T14:05:02Z
2025-02
2025-04-03T14:06:11.697Z
https://hdl.handle.net/1721.1/159091
Krylov subspace methods, like the Arnoldi iteration, are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we analyze the convergence of Krylov methods for estimating the numerical range of a matrix. Prior bounds on approximation error often depend on eigenvalue gaps of the matrix, which lead to weaker bounds than observed in practice, specifically in applications where these gaps are small. Instead, we extend a line of work proving gap-independent bounds for the Lanczos method, which depend only on the matrix dimensions and number of iterations, to the more general Arnoldi case.
M.Eng.
Massachusetts Institute of Technology
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Copyright retained by author(s)
https://creativecommons.org/licenses/by-nc-nd/4.0/
Convergence of the Arnoldi Iteration for Estimating Extreme Eigenvalues
Thesis
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
application/pdf
Master
Master of Engineering in Electrical Engineering and Computer Science
Publication
unknown
unknown
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