Related papers: Overlapping Schwarz Preconditioners for Pose-Graph…
In Simultaneous Localization And Mapping (SLAM) problems, high-level landmarks have the potential to build compact and informative maps compared to traditional point-based landmarks. In this work, we focus on the parameterization of…
Camera relocalization is the key component of simultaneous localization and mapping (SLAM) systems. This paper proposes a learning-based approach, named Sparse Spatial Scene Embedding with Graph Neural Networks (S3E-GNN), as an end-to-end…
Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the…
Multi-camera systems have been shown to improve the accuracy and robustness of SLAM estimates, yet state-of-the-art SLAM systems predominantly support monocular or stereo setups. This paper presents a generic sparse visual SLAM framework…
Simultaneous localization and mapping (SLAM) plays a vital role in mapping unknown spaces and aiding autonomous navigation. Virtually all state-of-the-art solutions today for 2D SLAM are designed for dense and accurate sensors such as laser…
We propose a novel dense mapping framework for sparse visual SLAM systems which leverages a compact scene representation. State-of-the-art sparse visual SLAM systems provide accurate and reliable estimates of the camera trajectory and…
The Virtual Element Method (VEM) is used to perform the discretization of the Poisson problem on polygonal and polyhedral meshes. This results in a symmetric positive definite linear system, which is solved iteratively using overlapping…
Two-level domain decomposition methods are preconditioned Krylov solvers. What separates one- and two-level domain decomposition methods is the presence of a coarse space in the latter. The abstract Schwarz framework is a formalism that…
Simultaneous Localization and Mapping (SLAM) has wide robotic applications such as autonomous driving and unmanned aerial vehicles. Both computational efficiency and localization accuracy are of great importance towards a good SLAM system.…
In this paper, we partially answer open questions about the convergence of overlapping Schwarz methods. We prove that overlapping Schwarz methods with Dirichlet transmission conditions for semilinear elliptic and parabolic equations always…
Pose graph optimization (PGO) is a well-known technique for solving the pose-based simultaneous localization and mapping (SLAM) problem. In this paper, we represent the rotation and translation by a unit quaternion and a three-dimensional…
In commercial autonomous service robots with several form factors, simultaneous localization and mapping (SLAM) is an essential technology for providing proper services such as cleaning and guidance. Such robots require SLAM algorithms…
In this paper, based on the overlapping domain decomposition method (DDM) proposed in \cite{Leng2015}, an one step preconditioner is proposed to solve 2D high frequency Helmholtz equation. The computation domain is decomposed in both $x$…
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 non-local exchange and scattering operators arising in domain decomposition algorithms for solving elliptic problems on domains in $\mathbb{R}^2$. Motivated by recent formulations of the Optimized Schwarz Method introduced by…
Reduced basis methods build low-rank approximation spaces for the solution sets of parameterized PDEs by computing solutions of the given PDE for appropriately selected snapshot parameters. Localized reduced basis methods reduce the offline…
We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method (BEM) for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as…
We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains that have arbitrary geometric and topological…
Pose graph relaxation has become an indispensable addition to SLAM enabling efficient global registration of sensor reference frames under the objective of satisfying pair-wise relative transformation constraints. The latter may be given by…
Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear…