3 citations · 3 across the 6 of their papers we have counts for
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Theoretical Analysis of Thermodynamic Matrix Inversion: First-order Equivalence to Preconditioned Gradient Descent and Implications for Analog Computing
Gerhard Kirsten, Michael Selby, Janith Petangoda +3
Recent research has demonstrated the possibility of exploiting the thermodynamics of coupled electrical oscillators to implement computational tasks such as matrix inversion. While…
A Tensor Train Approach for Deterministic Arithmetic Operations on Discrete Representations of Probability Distributions
Gerhard Kirsten, Bilgesu Bilgin, Janith Petangoda +1
Computing with discrete representations of high-dimensional probability distributions is fundamental to uncertainty quantification, Bayesian inference, and stochastic modeling. How…
A multilinear HJB-POD method for the optimal control of PDEs
Gerhard Kirsten, Luca Saluzzi
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging probl…
Multilinear POD-DEIM model reduction for 2D and 3D semilinear systems of differential equations
Gerhard Kirsten
We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take…
A matrix-oriented POD-DEIM algorithm applied to semilinear matrix differential equations
Gerhard Kirsten, Valeria Simoncini
We are interested in numerically approximating the solution of the large dimensional semilinear matrix differential equation $\dot{\bf U}(t) = { \bf A}{\bf U}(t) + {\b…
Order reduction methods for solving large-scale differential matrix Riccati equations
Gerhard Kirsten, Valeria Simoncini
We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen…