Through the Kaleidoscope: Symmetries,Groups and Chebyshev-Approximationsfrom a Computational Point of View
Hans Z. Munthe-Kaas, Morten Nome and Brett N. RylandDepartment of Mathematics, University of Bergen
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 towards 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. ...