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The Iterative Closest Point (ICP) algorithm is a crucial component of LiDAR-based SLAM algorithms. However, its performance can be negatively affected in unstructured environments that lack features and geometric structures, leading to low…

Robotics · Computer Science 2025-06-03 Haosong Yue , Qingyuan Xu , Fei Chen , Jia Pan , Weihai Chen

Pseudospectral methods represent an efficient approach for solving optimal control problems. While Legendre-Gauss-Lobatto (LGL) collocation points have traditionally been considered inferior to Legendre-Gauss (LG) and Legendre-Gauss-Radau…

Systems and Control · Electrical Eng. & Systems 2025-07-03 Yilin Zou , Fanghua Jiang

We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the…

Numerical Analysis · Mathematics 2020-07-15 Abele Simona , Luca Bonaventura , Carlo de Falco , Sebastian Schöps

Isogeometric analysis (IGA) is a numerical method that connects computer-aided design (CAD) with finite element analysis (FEA). In CAD the computational domain is usually represented by B-spline or NURBS patches. Given a NURBS…

Numerical Analysis · Mathematics 2023-10-04 Somayeh Kargaran , Bert Jüttler , Thomas Takacs

The lattice Boltzmann method has become a widely adopted approach in computational fluid dynamics, offering unique advantages in mesoscopic kinetic modeling, intrinsic parallelism, and simple treatment of boundary conditions. However, its…

Numerical Analysis · Mathematics 2025-09-16 Ye Ji , Monica Lacatus , Matthias Möller

This paper considers the multi-agent distributed linear least-squares problem. The system comprises multiple agents, each agent with a locally observed set of data points, and a common server with whom the agents can interact. The agents'…

Optimization and Control · Mathematics 2020-12-01 Kushal Chakrabarti , Nirupam Gupta , Nikhil Chopra

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the…

Numerical Analysis · Mathematics 2020-01-30 Jochen Hinz , Andrzej Jaeschke , Matthias Möller , Cornelis Vuik

In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We do so by incorporating the concept of discrete least…

Numerical Analysis · Mathematics 2021-02-24 Jan Glaubitz , Philipp Oeffner

The design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to the spline degree. Here, we analyze the application of…

Numerical Analysis · Mathematics 2018-06-18 Álvaro Pé de la Riva , Carmen Rodrigo , Francisco J. Gaspar

The strong-form asymmetric kernel-based collocation method, commonly referred to as the Kansa method, is easy to implement and hence is widely used for solving engineering problems and partial differential equations despite the lack of…

Numerical Analysis · Mathematics 2018-01-03 Ka-Chun Cheung , Leevan Ling , Robert Schaback

Future e-mobility calls for efficient electrical machines. For different areas of operation, these machines have to satisfy certain desired properties that often depend on their design. Here we investigate the use of multipatch Isogeometric…

Numerical Analysis · Mathematics 2026-04-02 Peter Gangl , Ulrich Langer , Angelos Mantzaflaris , Rainer Schneckenleitner

Solving an integer least squares (ILS) problem usually consists of two stages: reduction and search. This thesis is concerned with the reduction process for the ordinary ILS problem and the ellipsoid-constrained ILS problem. For the…

Optimization and Control · Mathematics 2015-03-17 Mazen Al Borno

We consider the isogeometric analysis for fractional PDEs involving the fractional Laplacian in two dimensions. An isogeometric collocation method is developed to discretize the fractional Laplacian and applied to the fractional Poisson…

Numerical Analysis · Mathematics 2020-05-12 Kailai Xu , Eric Darve

We introduce a novel quadrature strategy for Isogeometric Analysis (IgA) boundary element discretizations, specifically tailored to collocation methods. Thanks to the dimensionality reduction and the natural handling of unbounded domains,…

Numerical Analysis · Mathematics 2025-11-25 Cesare Bracco , Francesco Patrizi , Alessandra Sestini

This draft concerns the error analysis of a collocation method based on the moving least squares (MLS) approximation for integral equations, which improves the results of [2] in the analysis part. This is mainly a translation from Persian…

Numerical Analysis · Mathematics 2015-09-01 Davoud Mirzaei

Iteratively Re-weighted Least Squares (IRLS) is a method for solving minimization problems involving non-quadratic cost functions, perhaps non-convex and non-smooth, which however can be described as the infimum over a family of quadratic…

Numerical Analysis · Mathematics 2016-02-24 Massimo Fornasier , Steffen Peter , Holger Rauhut , Stephan Worm

This work studies the location estimation problem for a mixture of two rotation invariant log-concave densities. We demonstrate that Least Squares EM, a variant of the EM algorithm, converges to the true location parameter from a randomly…

Machine Learning · Statistics 2019-06-21 Wei Qian , Yuqian Zhang , Yudong Chen

This paper proposes and develops new linesearch methods with inexact gradient information for finding stationary points of nonconvex continuously differentiable functions on finite-dimensional spaces. Some abstract convergence results for a…

Optimization and Control · Mathematics 2023-01-03 Pham Duy Khanh , Boris S. Mordukhovich , Dat Ba Tran

In this paper, we present the first reduced basis method well-suited for the collocation framework. Two fundamentally different algorithms are presented: the so-called Least Squares Reduced Collocation Method (LSRCM) and Empirical Reduced…

Numerical Analysis · Mathematics 2012-08-27 Yanlai Chen , Sigal Gottlieb

Unfitted mesh formulations for interface problems generally adopt two distinct methodologies: (i) penalty-based approaches and (ii) explicit enrichment space techniques. While Stable Generalized Finite Element Method (SGFEM) has been…

Numerical Analysis · Mathematics 2025-03-21 Yin Song , Wenkai Hu , Xin Li