In our talk, we will present a new method for evaluating high order divided
differences for certain classes of analytic, possibly, operator valued
functions.
This is a classical problem in numerical mathematics but also arises in new
applications such as, e.g., the use of generalized convolution quadrature
to solve retarded potential integral equations.
The functions which we will consider are allowed to grow exponentially
to the left complex half plane and the interpolation points are scattered
in a large real interval. Our approach is based on the representation of
divided differences as contour integral and we will employ a subtle
parameterization of the contour in combination with a quadrature
approximation by the trapezoidal rule.
This talk comprises joint work with Dr Maria Lopez-Fernandez.

[invited by J.-P. Berrut and J.-P. Gabriel]