5 papers
A comparison of limited-memory Krylov methods for Stieltjes functions of Hermitian matrices
Stefan Güttel, Marcel Schweitzer
Given a limited amount of memory and a target accuracy, we propose and compare several polynomial Krylov methods for the approximation of f(A)b, the action of a Stieltjes matrix fu…
ABBA: Adaptive Brownian bridge-based symbolic aggregation of time series
Steven Elsworth, Stefan Güttel
A new symbolic representation of time series, called ABBA, is introduced. It is based on an adaptive polygonal chain approximation of the time series into a sequence of tuples, fol…
Time Series Forecasting Using LSTM Networks: A Symbolic Approach
Steven Elsworth, Stefan Güttel
Machine learning methods trained on raw numerical time series data exhibit fundamental limitations such as a high sensitivity to the hyper parameters and even to the initialization…
Algorithms for the rational approximation of matrix-valued functions
Ion Victor Gosea, Stefan Güttel
A selection of algorithms for the rational approximation of matrix-valued functions are discussed, including variants of the interpolatory AAA method, the RKFIT method based on app…
Limited-memory polynomial methods for large-scale matrix functions
Stefan Güttel, Daniel Kressner, Kathryn Lund
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various li…