Synergies

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.

• Read more about Exponential analysis in Computational Science and Engineering

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.

• Read more about Interplay between computational mathematics, sciences and other branches of mathematics

Integer matrices are often characterized by the lattice of combinations of their rows or columns.

• Read more about Eigenvalues, invariant factors and algorithms for sparse integer matrices

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.

• Read more about Low-rank updates of matrix functions

Estimating the spectral information of an exponential sum plays an important role in many signal processing applications.

• Read more about Identification problems in exponential analysis

In signal processing data are traditionally sampled according to the Shannon-Nyquist theorem in order to prevent aliasing effects.

• Read more about Validated Exponential Analysis

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.

• Read more about Working with rational functions in a numeric environment - some contributions

Reconstructing a digital signal from its measurements is an inverse problem that can be extremely ill-posed.

• Read more about How sub-sampling leads to more robustness and higher resolution in signal processing

Rational functions like for instance Padé approximants play an important role in signal processing, sparse interpolation and exponential analysis.

• Read more about Some contributions to controlling the presence of Froissart doublets in rational functions

Padé approximants play an important role in signal processing, sparse interpolation and exponential analysis.

• Read more about On the conditioning of the Padé map and related questions

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.

• Read more about A generalized Prony method for sparse approximation

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.

• Read more about Sparse interpolation and its connections to Padé approximation, signal processing, and tensor decomposition

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.

• Read more about Sparse wavelet approximation of signals and images

Throughout computational science and engineering, several attempts have been made to represent data in a parsimonious way.

• Read more about Sparse interpolation

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.

• Read more about Sparse approximation of signals and images