Related papers: Experimental Study of a Parallel Iterative Solver …
In this work, several multilevel decoupled algorithms are proposed for a mixed Navier-Stokes/Darcy model. These algorithms are based on either successively or parallelly solving two linear subdomain problems after solving a coupled…
Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…
Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved…
We iteratively derive the product-form solutions of stationary distributions of priority multiclass queueing networks with multi-sever stations. The networks are Markovian with exponential interarrival and service time distributions. These…
This paper proposes a parallelizable algorithm for linear-quadratic model predictive control (MPC) problems with state and input constraints. The algorithm itself is based on a parallel MPC scheme that has originally been designed for…
Simultaneous stabilization problem arises in various systems and control applications. This paper introduces a new approach to addressing this problem in the multivariable scenario, building upon our previous findings in the scalar case.…
We present a novel algorithm to solve a non-linear system of equations, whose solution can be interpreted as a tight lower bound on the vector of expected hitting times of a Markov chain whose transition probabilities are only partially…
In this work, we propose a parallel-in-time solver for linear and nonlinear ordinary differential equations. The approach is based on an efficient multilevel solver of the Schur complement related to a multilevel time partition. For linear…
Constraint problems can be trivially solved in parallel by exploring different branches of the search tree concurrently. Previous approaches have focused on implementing this functionality in the solver, more or less transparently to the…
Model checking has been proposed as a formal verification approach for analyzing computer-based and cyber-physical systems. The state space explosion problem is the main obstacle for applying this approach for sophisticated systems.…
The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…
In Markov-chain Monte Carlo simulations, estimating statistical errors or confidence intervals of numerically obtained values is an essential task. In this paper, we review several methods for error estimation, such as simple empirical…
This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…
Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In…
A weighted version of the parareal method for parallel-in-time computation of time dependent problems is presented. Linear stability analysis for a scalar weighing strategy shows that the new scheme may enjoy favorable stability properties…
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast…
We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large;…
In the following, we discuss nonlinear simulations of nonlinear dynamical systems, which are applied in technical and biological models. We deal with different ideas to overcome the treatment of the nonlinearities and discuss a novel…
Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a…
Models coming from different physical applications are very large in size. Simulation with such systems is expensive so one usually obtains a reduced model (by model reduction) that replicates the input-output behaviour of the original full…