相关论文: Multirate Exponential Rosenbrock Methods

In this paper, we propose and analyse a novel class of exponential collocation methods for solving conservative or dissipative systems based on exponential integrators and collocation methods. It is shown that these novel methods can be of…

The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…

Seismic imaging is a major challenge in geophysics with broad applications. It involves solving wave propagation equations with absorbing boundary conditions (ABC) multiple times. This drives the need for accurate and efficient numerical…

In this paper, we consider the classical robust adaptive beamforming (RAB) problem. Conventionally, this problem is solved either with an off-the-shelf solver like MOSEK or through the well-known RMVB algorithm based on Lagrange multiplier…

A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…

Matrix differential Riccati equation (DRE) typically exhibits transient and steady-state phases, posing challenges for fixed-step time integration methods, which may lack accuracy during transients or oversample in steady regimes. In this…

This paper proposes an implicit family of sub-step integration algorithms grounded in the explicit singly diagonally implicit Runge-Kutta (ESDIRK) method. The proposed methods achieve third-order consistency per sub-step and thus the…

We present algorithms for real and complex dot product and matrix multiplication in arbitrary-precision floating-point and ball arithmetic. A low-overhead dot product is implemented on the level of GMP limb arrays; it is about twice as fast…

We present a class of reduced basis (RB) methods for the iterative solution of parametrized symmetric positive-definite (SPD) linear systems. The essential ingredients are a Galerkin projection of the underlying parametrized system onto a…

The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…

Restricted Boltzmann machines (RBMs) are energy-based models analogous to the Ising model and are widely applied in statistical machine learning. The standard inverse Ising problem with a complete dataset requires computing both data and…

We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…

The randomized projection (RP) method is a simple iterative scheme for solving linear feasibility problems and has recently gained popularity due to its speed and low memory requirement. This paper develops an accelerated variant of the…

Finding robot poses and trajectories represents a foundational aspect of robot motion planning. Despite decades of research, efficiently and robustly addressing these challenges is still difficult. Existing approaches are often plagued by…

Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…

In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for solving initial-value problems of systems of ordinary…

Robust Markov Decision Processes (MDPs) are a powerful framework for modeling sequential decision-making problems with model uncertainty. This paper proposes the first first-order framework for solving robust MDPs. Our algorithm interleaves…

In this paper, we address the problem of reconfiguring Earth observation satellite constellation systems through multiple stages. The Multi-stage Constellation Reconfiguration Problem (MCRP) aims to maximize the total observation rewards…

Model usage is the central challenge of model-based reinforcement learning. Although dynamics model based on deep neural networks provide good generalization for single step prediction, such ability is over exploited when it is used to…

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible…