Multi-exponential analysis might sound remote, but it touches our lives in many surprising ways, even if most people are unaware of just how important it is.
The talk will start with a brief introduction of US NSF's 10 Big Ideas and give an overview of the recent trend of computational mathematics in the US.
Integer matrices are often characterized by the lattice of combinations of their rows or columns.
We consider the task of updating a matrix function f(A) when the matrix A ∈ Cnxn is subject to a low-rank modification. In other words, we aim at approximating f(A+D)-f(A) for a matrix D of rank k ≪ n.
Estimating the spectral information of an exponential sum plays an important role in many signal processing applications.
In signal processing data are traditionally sampled according to the Shannon-Nyquist theorem in order to prevent aliasing effects.
Rational functions like for instance Padé approximants play an important role in signal processing, sparse interpolation and exponential analysis. They have good theoretical properties in approximation and modeling.
Reconstructing a digital signal from its measurements is an inverse problem that can be extremely ill-posed.
Rational functions like for instance Padé approximants play an important role in signal processing, sparse interpolation and exponential analysis.
Padé approximants play an important role in signal processing, sparse interpolation and exponential analysis.
We derive a new generalization of Prony's method to reconstruct M-sparse expansions of (generalized) eigenfunctions of linear operators from only O(M) suitable values in a deterministic way.
Series of five research lectures for graduate students and researchers.
A mathematical model is called sparse if it is a combination of only a few non-zero terms.
Within the last time, various adaptive methods for signal and image approximation have been suggested. Instead of choosing a priori a basis or a frame to approximate an image, one tries to adapt the approximation scheme to the image geometry.
Throughout computational science and engineering, several attempts have been made to represent data in a parsimonious way.
A crucial problem in data analysis is to construct efficient low-level representations of mathematical objects from discrete signal data while preserving characteristic properties of the target object.