Two-dimensional Chebfuns and applications to matrix functions

• Applicant: Professor Dr. Stefan Dietrich Güttel
• Subject Area: Mathematics
• Term: from 2011 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 196671403

Chebfun is an object-oriented Matlab extension for computing with functions and operators instead of vectors and matrices. It is based on piecewise polynomial interpolation at Chebyshev nodes on real intervals. This research aims at extending Chebfun for functions defined on two-dimensional regions such as, e.g., polygons. Bivariate Chebyshev expansions constitute a promising approach towards achieving this goal, but the representation of sufficiently complicated functions requires the appropriate partitioning of the domain of definition, which should be done automatic and fast. Another issue is the development and implementation of robust algorithms for operations on two-dimensional Chebfuns, such as differentiation and root finding. A subproject explores the use of polynomial or rational Chebyshev expansions for the fast approximation of matrix function. Research is necessaryfor developing suitable stopping criteria of the associated iterative methods and for computing functions of nonnormal matrices.

• DFG Programme: Research Fellowships
• International Connection: United Kingdom
• Host: Professor Dr. Nick Trefethen