相关论文: Isogeometric Least-squares Collocation Method with…
Isospectral flows are abundant in mathematical physics; the rigid body, the the Toda lattice, the Brockett flow, the Heisenberg spin chain, and point vortex dynamics, to mention but a few. Their connection on the one hand with integrable…
Modern robotic systems are required to operate in challenging environments, which demand reliable localization under challenging conditions. LiDAR-based localization methods, such as the Iterative Closest Point (ICP) algorithm, can suffer…
The basic formal and numerical aspects of different degree interpolated moving least-squares (IMLS) methods are studied using sixteen different combinations of coordinate system for fitting and weight functions. For the application we use…
We propose a new discontinuous Galerkin Isogeometric Analysis (IgA) technique for the numerical solution of elliptic diffusion problems in computational domains decomposed into volumetric patches with non-matching interfaces. Due to an…
We present a fully explicit dynamic formulation for geometrically exact shear-deformable beams. The starting point of this work is an existing isogeometric collocation (IGA-C) formulation which is explicit in the strict sense of the time…
The approximation of tensors has important applications in various disciplines, but it remains an extremely challenging task. It is well known that tensors of higher order can fail to have best low-rank approximations, but with an important…
Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
We consider polynomial approximation over the interval $[-1,1]$ by regularized weighted discrete least squares methods with $\ell_2-$ or $\ell_1-$regularization, respectively. As the set of nodes we use Gauss quadrature points (which are…
Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…
Existing LGL methods typically consider only partial information (e.g., geometric features) from LiDAR observations or are designed for homogeneous LiDAR sensors, overlooking the uniformity in LGL. In this work, a uniform LGL method is…
An Orthogonal Least Squares (OLS) based feature selection method is proposed for both binomial and multinomial classification. The novel Squared Orthogonal Correlation Coefficient (SOCC) is defined based on Error Reduction Ratio (ERR) in…
In this paper, we present a progressive and iterative approximation method with memory for least square fitting(MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with…
In recent studies on sparse modeling, $l_q$ ($0<q<1$) regularized least squares regression ($l_q$LS) has received considerable attention due to its superiorities on sparsity-inducing and bias-reduction over the convex counterparts. In this…
The study of quantum three-body problems has been centered on low-energy states that rely on accurate numerical approximation. Recently, isogeometric analysis (IGA) has been adopted to solve the problem as an alternative but more robust…
Pose-Graph optimization is a crucial component of many modern SLAM systems. Most prominent state of the art systems address this problem by iterative non-linear least squares. Both number of iterations and convergence basin of these…
In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization of domain geometry, then…
In our work, we consider the linear least squares problem for $m\times n$-systems of linear equations $Ax = b$, $m\geq n$, such that the matrix $A$ and right-hand side vector $b$ can vary within an interval $m\times n$-matrix and an…
We consider elliptic problems in multipatch isogeometric analysis (IGA) where the patch parameterizations may be singular. Specifically, we address cases where certain dimensions of the parametric geometry diminish as the singularity is…