检索结果-内蒙古大学图书馆

The 5th Asia-Pacific International Conference on Computational Methods in Engineering and the 11th Chinese National Conference on Computational Methods in Engineering(ICOME 2015)

作者： KS NG SM WONG WK CHEUNG YC HON School of Science and Technology Open University of Hong Kong Department of Clinical Oncology Pamela Youde Nethersole Eastern Hospital Department of Mathematics City University of Hong Kong

The success of radiotherapy treatment relies in accurately localizing the target region close to tumor as well as avoiding damage to the nearby healthy organ. In order to control the tumor growth and minimize side effects to the patient, it is crucial to make some substantial modifications on the patient's anatomy due to the reduction of the patient's weight;shrinkage of the tumor;and the edema of the tissue before the treatment. For surgery consideration, an efficient registration method to delineate the clinically critical objects in computed tomography images obtained from the radiation treatment process is needed. Over the last decades, the Deformable Image Registration Model has undergone intensive investigation from researchers in the fields of computer vision, remote sensing, and etc. Despite the significant progress that has been made, deformable registration remains a challenging problem in the field of radiotherapy. based on the recent development of Demons algorithm and kernel-based approximation method, we discuss in this paper a deformation image registration algorithm for the potential development of interactive deformable image registration package for surgery use. The performance in terms of both accuracy and efficiency of the proposed method will be compared and discussed.

关键词： Deformable Image Registration Demons Algorithm kernel-based approximation

来源：评论

学校读者我要写书评

暂无评论

Node-bound communities for partition of unity interpolation on graphs

引用

APPLIED MATHEMATICS AND COMPUTATION 2024年 467卷

作者： Cavoretto, Roberto De Rossi, Alessandra Lancellotti, Sandro Romaniello, Federico Univ Torino Dept Math Giuseppe Peano via Carlo Alberto I-10123 Turin Italy

Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a partition of unity solely based on the underlying graph structure, employing an algorithm that relies exclusively on centrality measures and modularity, without requiring the input of the number of subdomains. Subsequently, we integrate PUMs with a local graph basis function (GBF) approximation method to develop cost-effective global interpolation schemes. We also discuss numerical experiments conducted on both synthetic and real datasets to assess the performance of this presented technique.

关键词： Partition of unity methods kernel-based approximation Graph basis functions Graph signal processing Graph theory

来源：评论

学校读者我要写书评

暂无评论

Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation

引用

ADVANCES IN COMPUTATIONAL MATHEMATICS 2025年第2期51卷 1-27页

作者： Albrecht, Kristof Entzian, Juliane Iske, Armin Univ Hamburg Dept Math Hamburg Germany

This work concerns the construction and characterization of product kernels for multivariate approximation from a finite set of discrete samples. To this end, we consider composing different component kernels, each acting on a low-dimensional Euclidean space. Due to Aronszajn (Trans. Am. Math. Soc. 68, 337-404 1950), the product of positive semi-definite kernel functions is again positive semi-definite, where, moreover, the corresponding native space is a particular instance of a tensor product, referred to as Hilbert tensor product. We first analyze the general problem of multivariate interpolation by product kernels. Then, we further investigate the tensor product structure, in particular for grid-like samples. We use this case to show that the product of positive definite kernel functions is again positive definite. Moreover, we develop an efficient computation scheme for the well-known Newton basis. Supporting numerical examples show the good performance of product kernels, especially for their flexibility.

关键词： kernel-based approximation Product kernels Greedy algorithms

来源：评论

学校读者我要写书评

暂无评论

Bayesian approach for radial kernel parameter tuning

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2024年 441卷

作者： Cavoretto, Roberto De Rossi, Alessandra Lancellotti, Sandro Univ Torino Dept Math Giuseppe Peano Via Carlo Alberto 10 I-10123 Turin Italy

In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as a special case, which enables us to effectively find the optimal value of the RBF shape parameter. In particular, we propose a statistical technique, called Bayesian optimization, that consists in modeling the error function with a Gaussian process, by which, through an iterative process, the optimal shape parameter is selected. The process is step by step self-updated resulting in a relevant decrease in search time with respect to the classical leave one out cross validation technique. Numerical results deriving from some test examples and an application to real data show the performance of the proposed method.

关键词： Radial basis function interpolation kernel-based approximation Shape parameter Bayesian optimization Hyper-parameter search

来源：评论

学校读者我要写书评

暂无评论

A MESHFREE METHOD FOR A PDE-CONSTRAINED OPTIMIZATION PROBLEM

引用

SIAM JOURNAL ON NUMERICAL ANALYSIS 2021年第4期59卷 1896-1917页

作者： Hoff, Daniel Wendland, Holger Tech Univ Ilmenau Inst Math D-98694 Ilmenau Germany Univ Bayreuth Dept Math Appl & Numer Anal D-95440 Bayreuth Germany

We describe a new approximation method for solving a PDE-constrained optimization problem numerically. Our method is based on the adjoint formulation of the optimization problem, leading to a system of weakly coupled, elliptic PDEs. These equations are then solved using kernel-based collocation. We derive an error analysis and give numerical examples.

关键词： PDE-constrained optimization radial basis functions meshfree methods kernel-based approximation error analysis

来源：评论

学校读者我要写书评

暂无评论

kernel-based approximation for Cauchy problem of the time-fractional diffusion equation

引用

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2012年第9期36卷 1344-1352页

作者： Dou, F. F. Hon, Y. C. City Univ Hong Kong Dept Math Hong Kong Hong Kong Peoples R China Univ Elect Sci & Technol China Sch Math Sci Chengdu 610054 Peoples R China

We investigate in this paper a Cauchy problem for the time-fractional diffusion equation (TFDE). based on the idea of kernel-based approximation, we construct an efficient numerical scheme for obtaining the solution of a Cauchy problem of TFDE. The use of M-Wright functions as the kernel functions for the approximation space allows us to express the solution in terms of M-Wright functions, whose numerical evaluation can be accurately achieved by applying the inverse Laplace transform technique. To handle the ill-posedness of the resultant coefficient matrix due to the noisy Cauchy data, we adapt the standard Tikhonov regularization technique with the L-curve method for obtaining the optimal regularization parameter to give a stable numerical reconstruction of the solution. Numerical results indicate the efficiency and effectiveness of the proposed scheme. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Cauchy problem of time-fractional diffusion equation kernel-based approximation Fundamental solution Inverse Laplace transform Tikhonov regularization L-curve

来源：评论

学校读者我要写书评

暂无评论

AN IMPROVED CONVERGENCE RESULT FOR THE SMOOTHED PARTICLE HYDRODYNAMICS METHOD

引用

SIAM JOURNAL ON MATHEMATICAL ANALYSIS 2021年第2期53卷 1239-1262页

作者： Franz, Tino Wendland, Holger Univ Bayreuth Dept Math Appl & Numer Anal D-95440 Bayreuth Germany

The smoothed particle hydrodynamics (SPH) method is a popular, kernel-based discretization method for fluid-flow problems. Despite its frequent use, mathematical understanding is still limited. In [T. Franz and H. Wendland, SIAM J. Math. Anal., 50 (2018), pp. 4752--4784] we proved convergence for a specific flow problem under appropriate conditions on the underlying kernel. The kernel has to satisfy so-called moment and approximation conditions. We also showed that the generalized Wendland kernels satisfy these conditions in odd space dimensions. In this paper, we will significantly improve the above results in the following ways. We will show that the results also hold in even space dimensions. We will show that the generalized Wendland kernels satisfy the approximation condition of any order, which means that for these kernels we can eliminate the dependence of the convergence rate on the approximation condition. We will show that the standard Wendland kernels, though they perform numerically similarly, do not satisfy the approximation condition.

关键词： SPH Euler equations convergence analysis kernel-based approximation

来源：评论

学校读者我要写书评

暂无评论

The Role of Hilbert-Schmidt SVD basis in Hermite-Birkhoff interpolation in fractional sense

引用

COMPUTATIONAL & APPLIED MATHEMATICS 2019年第2期38卷 1-20页

作者： Esmaeilbeigi, M. Chatrabgoun, O. Cheraghi, M. Malayer Univ Fac Math Sci & Stat Dept Math Malayer *** Iran Malayer Univ Fac Math Sci & Stat Dept Stat Malayer *** Iran

The Hermite-Birkhoff (HB) interpolation is an extension of polynomial interpolation that appears when observation gives operational information. Additional capabilities in HB interpolation by considering fractional operators are created, as it occur in many applied systems. Due to the nice properties in kernel-based approximation, we intend to apply it to solve the HB interpolation in the fractional sense. We show the standard basis in kernel-based approximation is often insufficient for computing a stable solution in fractional HB interpolation. Because of the inherent ill-condition of kernel-based methods, we investigate the fractional HB interpolation using alternate Hilbert-Schmidt SVD (HS-SVD) bases, since it provides a linear transformation which can be applied analytically, and therefore, is able to remove a significant portion of the ill-conditioning. Also, the convergence and stability of the fractional HB interpolation using HS-SVD method are discussed. Numerical results show that in solving fractional HB interpolation, although the standard basis for many positive definite kernels is ill-conditioned in the flat limit, the HS-SVD basis solves the existing problem.

关键词： Hermite-Birkhoff interpolation Fractional derivatives Hilbert-Schmidt SVD method kernel-based approximation

来源：评论

学校读者我要写书评

暂无评论

CONVERGENCE OF THE SMOOTHED PARTICLE HYDRODYNAMICS METHOD FOR A SPECIFIC BAROTROPIC FLUID FLOW: CONSTRUCTIVE kernel THEORY

引用

SIAM JOURNAL ON MATHEMATICAL ANALYSIS 2018年第5期50卷 4752-4784页

作者： Franz, Tino Wendland, Holger Univ Bayreuth Appl & Numer Anal Dept Math D-95440 Bayreuth Germany

Smoothed particle hydrodynamics (SPH) is a popular particle- and kernel-based method for numerically computing solutions to fluid-flow problems. In this paper, we study the convergence of SPH for the Euler equations of a specific barotropic fluid. In contrast to previous works, we distinguish carefully between the smoothing and the discretization parameters and give explicit relations between both of them to guarantee convergence. This convergence heavily depends on certain properties of the underlying kernel. Hence, a large part of this paper is devoted to constructing compactly supported, radial kernels which possess the required properties.

关键词： Euler equations smoothed particle hydrodynamics convergence analysis kernel-based approximation

来源：评论

学校读者我要写书评

暂无评论

Image reconstruction from scattered Radon data by weighted positive definite kernel functions

引用

CALCOLO 2018年第1期55卷 2-2页

作者： De Marchi, S. Iske, A. Santin, G. Univ Padua Dept Math Padua Italy Univ Hamburg Dept Math Hamburg Germany Univ Stuttgart Inst Appl Anal & Numer Simulat Stuttgart Germany

We propose a novel kernel-based method for image reconstruction from scattered Radon data. To this end, we employ generalized Hermite-Birkhoff interpolation by positive definite kernel functions. For radial kernels, however, a straightforward application of the generalized Hermite-Birkhoff interpolation method fails to work, as we prove in this paper. To obtain a well-posed reconstruction scheme for scattered Radon data, we introduce a new class of weighted positive definite kernels, which are symmetric but not radially symmetric. By our construction, the resulting-weighted kernels are combinations of radial positive definite kernels and positive weight functions. This yields very flexible image reconstruction methods, which work for arbitrary distributions of Radon lines. We develop suitable representations for the weighted basis functions and the symmetric positive definite kernel matrices that are resulting from the proposed reconstruction scheme. For the relevant special case, where Gaussian radial kernels are combined with Gaussian weights, explicit formulae for the weighted Gaussian basis functions and the kernel matrices are given. Supporting numerical examples are finally presented.

关键词： Image reconstruction kernel-based approximation Generalized Hermite-Birkhoff interpolation Radon transform Positive definite kernels

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：