Dear GMS,
I hope you are doing well.
We will have a seminar on Monday, March 23, between 11:30 and 12:30 at 225 St. Paul's.
Our speaker will be @Gabriel Hammmailto:hammg2@myumanitoba.ca. You can find more information about his talk below.
Title: Fast algorithms for Sobolev orthogonal polynomials
Abstract: Sobolev orthogonal polynomials are those polynomials orthogonal with respect to an inner product including derivatives. They have a beautiful and rich theoretical history. We propose fast algorithms for Sobolev orthogonal polynomials by careful consideration of the properties of the Sobolev–Gram matrix. We begin with a description of a matrix equation for the Sobolev–Gram matrix with a number of terms proportional to the order of the Sobolev inner product. We describe conditions on the vectorial measure that cause the Sobolev–Gram matrix to be banded, leading to linear complexity Cholesky factorization. Next, we convert the problem of including Dirac measures into that of a finite-rank perturbation of a known Cholesky factorization, which can also be performed in linear complexity. Finally, in the case of conversion to Chebyshev polynomials, we harness the power of randomized numerical linear algebra to solve the connection problem in O(n log^{O(1)}n) flops.
See you all in the seminar! GMS Websitehttps://sites.google.com/view/umgradmathsociety/ / Instagramhttps://www.instagram.com/umgradmathsociety/
Sincerely, Berkanthttps://cnnk.xyz GMS Executive