Related papers: A Progressive Statistical Method for Preconditioni…

This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…

The purpose of the current work is to find numerical solutions of the steady state inhomogeneous Vlasov equation. This problem has a wide range of applications in the kinetic simulation of non-thermal plasmas. However, the direct…

When solving linear systems with nonsymmetric Toeplitz or multilevel Toeplitz matrices using Krylov subspace methods, the coefficient matrix may be symmetrized. The preconditioned MINRES method can then be applied to this symmetrized…

For several classes of mathematical models that yield linear systems, the splitting of the matrix into its Hermitian and skew Hermitian parts is naturally related to properties of the underlying model. This is particularly so for…

Accumulating substantial volumes of real-world driving data proves pivotal in the realm of trajectory forecasting for autonomous driving. Given the heavy reliance of current trajectory forecasting models on data-driven methodologies, we aim…

In this paper, we consider the numerical solution of the poroelasticity problem with stochastic properties. We present a Two-stage Markov Chain Monte Carlo method for geomechanical subsidence. In this work, we study two techniques of…

In this paper, a novel augmented Lagrangian preconditioner based on global Arnoldi for accelerating the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure, these systems…

We propose a simple technique for verifying probabilistic models whose transition probabilities are parametric. The key is to replace parametric transitions by nondeterministic choices of extremal values. Analysing the resulting…

In this paper we study fast iterative solvers for the large sparse linear systems resulting from the stochastic Galerkin discretization of stochastic partial differential equations. A block triangular preconditioner is introduced and…

Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…

In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to…

Despite hundreds of papers on preconditioned linear systems of equations, there remains a significant lack of comprehensive performance benchmarks comparing various preconditioners for solving symmetric positive definite (SPD) systems. In…

This article analyzes the high-gain prediction approach for nonlinear input-delay systems. The problem is discussed in the light of weighted homogeneity and input-to-state stability. The canonical form for uniformly observable nonlinear…

We provide a rounding error analysis of a mixed-precision preconditioned Jacobi algorithm, which uses low precision to compute the preconditioner, applies it at high precision (amounting to two matrix-matrix multiplications) and solves the…

It is well-known that the convergence of Krylov subspace methods to solve linear system depends on the spectrum of the coefficient matrix, moreover, it is widely accepted that for both symmetric and unsymmetric systems Krylov subspace…

This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…

Randomized methods are becoming increasingly popular in numerical linear algebra. However, few attempts have been made to use them in developing preconditioners. Our interest lies in solving large-scale sparse symmetric positive definite…

We study a preconditioner for a Hermitian positive definite linear system, which is obtained as the solution of a matrix nearness problem based on the Bregman log determinant divergence. The preconditioner is of the form of a Hermitian…

Although design optimization has shown its great power of automatizing the whole design process and providing an optimal design, using sophisticated computational models, its process can be formidable due to a computationally expensive…

We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a low-dimensional subspace of operators by solving a small…