Article: Through the Kaleidoscope. Symmetries, Groups and Chebyshev Approximations from a Computational Point of View
Authors: H. Z. Munthe-Kaas, M. Nome, B. N. Ryland
Journal: Foundations of Computational Mathematics, Budapest 2011 403, 188. London Mathematical Society Lecture Note Series.
Abstract: In this paper we survey parts of group theory, with emphasis on structures that are important in design and analysis of numerical algorithms and in software design. In particular, we provide an extensive introduction to Fourier analysis on locally compact abelian groups, and point to- wards applications of this theory in computational mathematics. Fourier analysis on non-commutative groups, with applications, is discussed more briefly. In the final part of the paper we provide an introduction to multivariate Chebyshev polynomials. These are constructed by a kaleidoscope of mirrors acting upon an abelian group, and have recently been applied in numerical Clenshaw–Curtis type numerical quadrature and in spec- tral element solution of partial differential equations, based on triangular and simplicial subdivisions of the domain.
Hindsight notes: None yet.
5 Jan 2012