22 citations · 27 across the 14 of their papers we have counts for
14 papers
Error Bound and Stability Analysis for a Randomized Singly Diagonally Implicit Runge-Kutta Method
Monika Eisenmann, Marvin Jans, Raphael Kruse +1
A randomized Singly Diagonally Implicit Runge-Kutta (SDIRK) method, based on the randomized trapezoidal rule as the underlying quadrature scheme, is proposed. Every realization of…
Convergence analysis of Schwarz-like methods for degenerate elliptic-parabolic equations
Monika Eisenmann, Eskil Hansen
Convergence is proven for Schwarz-like methods applied to degenerate elliptic-parabolic equations with a -structure. This family of PDEs, e.g., arises when modelling nonlinear d…
Error bounds for full space-time splitting discretizations of semi-linear SPDEs -- with a focus on dG domain decompositions
Monika Eisenmann, Eskil Hansen, Marvin Jans
We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formula…
Analysis of a Class of Stochastic Component-Wise Soft-Clipping Schemes
Måns Williamson, Monika Eisenmann, Tony Stillfjord
Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms wil…
A domain decomposition method for stochastic evolution equations
Evelyn Buckwar, Ana Djurdjevac, Monika Eisenmann
In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, ou…
A randomized operator splitting scheme inspired by stochastic optimization methods
Monika Eisenmann, Tony Stillfjord
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination…
Sub-linear convergence of a tamed stochastic gradient descent method in Hilbert space
Monika Eisenmann, Tony Stillfjord
In this paper, we introduce the tamed stochastic gradient descent method (TSGD) for optimization problems. Inspired by the tamed Euler scheme, which is a commonly used method withi…
Sub-linear convergence of a stochastic proximal iteration method in Hilbert space
Monika Eisenmann, Tony Stillfjord, Måns Williamson
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the…
Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations
Monika Eisenmann, Mihály Kovács, Raphael Kruse +1
In this paper, we derive error estimates of the backward Euler-Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation i…
A variational approach to the sum splitting scheme
Monika Eisenmann, Eskil Hansen
Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an e…
Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data
Monika Eisenmann, Etienne Emmrich, Volker Mehrmann
For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert--Schmidt operators existence of solutions is studied. An exi…
Two quadrature rules for stochastic Itô-integrals with fractional Sobolev regularity
Monika Eisenmann, Raphael Kruse
In this paper we study the numerical quadrature of a stochastic integral, where the temporal regularity of the integrand is measured in the fractional Sobolev-Slobodeckij norm in $…
On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients
Monika Eisenmann, Mihály Kovács, Raphael Kruse +1
In this paper we introduce a randomized version of the backward Euler method, that is applicable to stiff ordinary differential equations and nonlinear evolution equations with tim…
Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations
Monika Eisenmann, Eskil Hansen
Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in g…