Related papers: Overlapping Schwarz Preconditioners for Pose-Graph…
We present an algebraic method for constructing a highly effective coarse grid correction to accelerate domain decomposition. The coarse problem is constructed from the original matrix and a small set of input vectors that span a low-degree…
Recently the dense Simultaneous Localization and Mapping (SLAM) based on neural implicit representation has shown impressive progress in hole filling and high-fidelity mapping. Nevertheless, existing methods either heavily rely on known…
In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
We analyze a multilevel diagonal additive Schwarz preconditioner for the adaptive coupling of FEM and BEM for a linear 2D Laplace transmission problem. We rigorously prove that the condition number of the preconditioned system stays…
This paper gives a unified convergence analysis of additive Schwarz methods for general convex optimization problems. Resembling to the fact that additive Schwarz methods for linear problems are preconditioned Richardson methods, we prove…
We deal with the numerical solution of linear elliptic problems with varying diffusion coefficient by the $hp$-discontinuous Galerkin method. We develop a two-level hybrid Schwarz preconditioner for the arising linear algebraic systems. The…
Medical endoscopy remains a challenging application for simultaneous localization and mapping (SLAM) due to the sparsity of image features and size constraints that prevent direct depth-sensing. We present a SLAM approach that incorporates…
Simultaneous Localization and Mapping (SLAM) is one of the most essential techniques in many real-world robotic applications. The assumption of static environments is common in most SLAM algorithms, which however, is not the case for most…
In this paper, we propose an optimization based SLAM approach to simultaneously optimize the robot trajectory and the occupancy map using 2D laser scans (and odometry) information. The key novelty is that the robot poses and the occupancy…
Traditional simultaneous localization and mapping (SLAM) methods focus on improvement in the robot's localization under environment and sensor uncertainty. This paper, however, focuses on mitigating the need for exact localization of a…
This paper introduces a novel optimization algorithm designed for nonlinear least-squares problems. The method is derived by preconditioning the gradient descent direction using the Singular Value Decomposition (SVD) of the Jacobian. This…
Fourth-order variational inequalities are encountered in various scientific and engineering disciplines, including elliptic optimal control problems and plate obstacle problems. In this paper, we consider additive Schwarz methods for…
Graph-SLAM is a well-established algorithm for constructing a topological map of the environment while simultaneously attempting the localisation of the robot. It relies on scan matching algorithms to align noisy observations along robot's…
The SLAM problem is known to have a special property that when robot orientation is known, estimating the history of robot poses and feature locations can be posed as a standard linear least squares problem. In this work, we develop a SLAM…
Recent research on problem formulations based on decomposition into low-rank plus sparse matrices shows a suitable framework to separate moving objects from the background. The most representative problem formulation is the Robust Principal…
Simultaneous localization and mapping (SLAM) is a critical capability in autonomous navigation, but in order to scale SLAM to the setting of "lifelong" SLAM, particularly under memory or computation constraints, a robot must be able to…
Simultaneous localization and mapping (SLAM) is a critical capability for autonomous systems. Traditional SLAM approaches, which often rely on visual or LiDAR sensors, face significant challenges in adverse conditions such as low light or…
Convergence is proven for Schwarz-like methods applied to degenerate elliptic-parabolic equations with a $p$-structure. This family of PDEs, e.g., arises when modelling nonlinear diffusion processes. The Schwarz-like approximation methods…
Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently in the context of problems for which Newton's method…