Wednesday, December 8, 2021
Time | Items |
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All day |
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2pm |
12/08/2021 - 2:30pm Abstract: The roots of a function represented by its Chebyshev expansion are known to be the eigenvalues of the so-called colleague matrix, which is a Hessenberg matrix that is the sum of a symmetric tridiagonal matrix and a rank 1 perturbation. The rootfinding problem is thus reformulated as an eigenproblem, making the computation of the eigenvalues of such matrices a subject of significant practical interest. To obtain the roots with the maximum possible accuracy, the eigensolver used must possess a somewhat subtle form of stability. In this talk, I will discuss a recently constructed algorithm for the diagonalization of colleague matrices, satisfying the relevant stability requirements. The scheme has CPU time requirements proportional to n^2, with n the dimensionality of the problem; the storage requirements are proportional to n. Furthermore, the actual CPU times (and storage requirements) of the procedure are quite acceptable, making it an approach of choice even for small-scale problems. I will illustrate the performance of the algorithm with several numerical examples. Location:
https://yale.zoom.us/j/97458245891
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4pm |
12/08/2021 - 4:00pm The Putnam seminar meets every Wednesday from 4 to 5:30 in LOM 214. As always, everyone is warmly welcomed to come to hang out, learn more cool math, and meet folks. The seminar is casual, and folks can come and go as they like. See Pat Devlin’s webpage (and/or contact him) for more information. Folks can sign up for the mailing list here: https://forms.gle/nYPx72KVJxJcgLha8 Location:
LOM 214
12/08/2021 - 4:15pm Given a fractal set $E$ on the plane and a set $F$ of directions, can we find one direction $\theta\in F$ such that the orthogonal projection $\Pi_{\theta} E$ is large? We will survey some classical and modern projection theorems and discuss their applications. Location: |