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Related papers: Overlapping Schwarz Preconditioners for Pose-Graph…

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We propose an efficient algorithm that combines overlapping domain decomposition and proper generalized decomposition (PGD) to construct surrogate models of linear elliptic parametric problems. The technique is composed of an offline and an…

Numerical Analysis · Mathematics 2024-09-16 Marco Discacciati , Ben J. Evans , Matteo Giacomini

We propose a nonlinear additive Schwarz method for solving nonlinear optimization problems with bound constraints. Our method is used as a "right-preconditioner" for solving the first-order optimality system arising within the sequential…

Optimization and Control · Mathematics 2024-02-07 Hardik Kothari , Alena Kopaničáková , Rolf Krause

We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and…

Numerical Analysis · Mathematics 2019-12-20 Carlos Echeverría , Jörg Liesen , Petr Tichý

We investigate the parallel one-level overlapping Schwarz method for solving finite element discretization of high-frequency Helmholtz equations. The resulting linear systems are large, indefinite, ill-conditioned, and complex-valued. We…

Numerical Analysis · Mathematics 2026-02-03 Yan Xie , Shihua Gong , Ivan G. Graham , Euan A. Spence , Chen-Song Zhang

We present a non-overlapping, Schwarz-type domain decomposition method with a generalized interface condition, designed for physics-informed machine learning of partial differential equations (PDEs) in both forward and inverse contexts. Our…

Machine Learning · Computer Science 2025-08-22 Qifeng Hu , Shamsulhaq Basir , Inanc Senocak

In this paper, we aim to design sparse D-optimal (determinantoptimal) pose-graph SLAM problems through the synthesis of sparse graphs with the maximum weighted number of spanning trees. Characterizing graphs with the maximum number of…

Robotics · Computer Science 2016-11-04 Kasra Khosoussi , Gaurav S. Sukhatme , Shoudong Huang , Gamini Dissanayake

Additive overlapping Schwarz Methods are iterative methods of the domain decomposition type for the solution of partial differential equations. Numerical and parallel scalability of these methods can be achieved by adding coarse levels. A…

Numerical Analysis · Mathematics 2026-05-06 Stephan Köhler , Oliver Rheinbach

We present a preconditioning method for the linear systems arising from the boundary element discretization of the Laplace hypersingular equation on a $2$-dimensional triangulated surface $\Gamma$ in $\mathbb{R}^3$. We allow $\Gamma$ to…

Numerical Analysis · Mathematics 2023-10-16 Martin Averseng , Xavier Claeys , Ralf Hiptmair

Monolithic preconditioners applied to the linear systems arising during the solution of the discretized incompressible Navier-Stokes equations are typically more robust than preconditioners based on incomplete block factorizations. Lower…

Numerical Analysis · Mathematics 2026-02-11 Alexander Heinlein , Axel Klawonn , Jascha Knepper , Lea Saßmannshausen

The two-level overlapping additive Schwarz method offers a robust and scalable preconditioner for various linear systems resulting from elliptic problems. One of the key to these properties is the construction of the coarse space used to…

Numerical Analysis · Mathematics 2024-08-16 Filipe A. C. S. Alves , Alexander Heinlein , Hadi Hajibeygi

Accelerating iterative eigenvalue algorithms is often achieved by employing a spectral shifting strategy. Unfortunately, improved shifting typically leads to a smaller eigenvalue for the resulting shifted operator, which in turn results in…

Numerical Analysis · Mathematics 2024-10-10 Lambert Theisen , Benjamin Stamm

This paper considers the collaborative graph exploration problem in GPS-denied environments, where a group of robots are required to cover a graph environment while maintaining reliable pose estimations in collaborative simultaneous…

Robotics · Computer Science 2024-07-02 Ruofei Bai , Shenghai Yuan , Hongliang Guo , Pengyu Yin , Wei-Yun Yau , Lihua Xie

One of the important aspects of IsoGeometric Analysis (IGA) is the strong link between Computer Aided Design and analysis. Two of IGA'a major challenge are the assembly of patches (Constructive Solid Geometry geometries made of Boolean…

Numerical Analysis · Mathematics 2015-02-13 Michel Bercovier , Ilya Soloveichik

Our research focuses on the development of domain decomposition preconditioners tailored for second-order elliptic partial differential equations. Our approach addresses two major challenges simultaneously: i) effectively handling…

Numerical Analysis · Mathematics 2023-06-28 Juan G. Calvo , Juan Galvis

Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…

Numerical Analysis · Mathematics 2022-01-10 Hussam Al Daas , Pierre Jolivet , Tyrone Rees

This paper introduces a fully algebraic two-level additive Schwarz preconditioner for general sparse large-scale matrices. The preconditioner is analyzed for symmetric positive definite (SPD) matrices. For those matrices, the coarse space…

Numerical Analysis · Mathematics 2024-01-09 Hussam Al Daas , Pierre Jolivet , Frédéric Nataf , Pierre-Henri Tournier

A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…

Numerical Analysis · Mathematics 2025-10-31 Simon Dirckx , Anna Yesypenko , Per-Gunnar Martinsson

Blending representation learning approaches with simultaneous localization and mapping (SLAM) systems is an open question, because of their highly modular and complex nature. Functionally, SLAM is an operation that transforms raw sensor…

Robotics · Computer Science 2020-11-20 Krishna Murthy Jatavallabhula , Soroush Saryazdi , Ganesh Iyer , Liam Paull

Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…

Computation · Statistics 2024-08-02 Haoyuan Chen , Rui Tuo

A symmetric and a nonsymmetric variant of the additive Schwarz preconditioner are proposed for the solution of a nonsymmetric system of algebraic equations arising from a general finite volume element discretization of symmetric elliptic…

Numerical Analysis · Mathematics 2018-06-14 Leszek Marcinkowski , Talal Rahman , Atle Loneland , Jan Valdman