日時 ： 2015年 12月10日(木) 17:30 ～ 18:30
場所 ： 東京大学 工学部 14号館 5階 534号室
http://www.u-tokyo.ac.jp/campusmap/cam01_04_15_j.
講演者：Jared Aurentz (University of Oxford)
Part 1タイトル：Fast algorithms for spectral differentiation matrices
講演概要：Recently Olver and Townsend presented a fast spectral method
that relies on bases of ultraspherical polynomials to give
differentiation matrices that are almost banded. The almost-banded
structure allowed them to develop efficient algorithms for solving
ceratin discretized systems in linear time. We show that one can also
design fast algorithms for standard spectral methods because the
underlying matrices, though dense, have the same rank structure as those
of Olver and Townsend.
Part 2 タイトル：Krylov methods for operators
講演概要：In this talk we will explore the convergence of Krylov methods
when used to solve $Lu = f$ where $L$ is an unbounded linear operator.
We will show that for certain problems, methods like Conjugate Gradients
and GMRES still converge even though the spectrum of $L$ is unbounded. A
theoretical justification for this behavior is given in terms of
polynomial approximation on unbounded domains.