Quadrature With Respect to Binomial Measures
Francesco Calabró, Antonio Corbo Esposito
本文研究二项式测度下的积分，发展了插值型求积规则并推导了局部误差估计。
本文致力于研究关于二项式测度的积分。我们发展了插值型求积规则并研究了它们的性质。在一般框架下推导了这些规则的局部误差估计。
This work is devoted to the study of integration with respect to binomial measures. We develop interpolatory quadrature rules and study their properties. Local error estimates for these rules are derived in a general framework.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We study the effects of numerical quadrature rules on error convergence rates when solving Maxwell-type variational problems via the curl-conforming or edge finite element method. A complete {\em a priori} error analysis for the case of bounded polygonal and curved domains with non-homogeneous coefficients is provided. We detail sufficient conditions with respect to mesh refinement and precision for the quadrature rules so as to guarantee convergence rates following that of exact numerical integration. On curved domains, we isolate the error contribution to numerical quadrature rules.
A unified generalization of some quadrature rules and error bounds
通过引入参数，统一推广了中点、梯形和辛普森等求积规则，得到了新的误差界。
Sparse Quadrature for High-Dimensional Integration with Gaussian Measure
本文分析了高维参数下基于高斯测度的稀疏求积法的维度无关收敛性，提出前验和后验方案并进行数值实验验证其收敛性。
Very high-order symmetric positive-interior quadrature rules on triangles and tetrahedra
本文提出三角形和四面体上最高84阶和40阶的全对称正权重内部节点积分规则，利用张量积初始猜测与节点消除方法实现高效构造，效率分别超过95%和80%。
Efficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for B-splines
本文提出加权高斯求积规则，用于B样条的高效质量与刚度矩阵组装，减少求积点数量并降低计算成本。
Efficient assembly based on B-spline tailored quadrature rules for the IgA-SGBEM
本文基于B-样条的定制四阶规则，提出高效的SGBEM-IgA方法，通过行装配和求和因子化提升求解效率，验证了在计算成本和时间上的优势。
A novel method is proposed to infer Bayesian predictions of computationally expensive models. The method is based on the construction of quadrature rules, which are well-suited for approximating the weighted integrals occurring in Bayesian prediction. The novel idea is to construct a sequence of nested quadrature rules with positive weights that converge to a quadrature rule that is weighted with respect to the posterior. The quadrature rules are constructed using a proposal distribution that is determined by means of nearest neighbor interpolation of all available evaluations of the posterior…
Gaussian quadrature rules for composite highly oscillatory integrals
针对电子工程中的复合高度振荡积分，提出两种Gauss求积规则，分别基于经典正交多项式理论和变号函数，并给出收敛性分析与数值验证。
Error Estimates with Explicit Constants for Sinc Quadrature and Sinc Indefinite Integration over Infinite Intervals
本文针对半无限和无限区间，给出了Sinc求积与Sinc不定积分的显式可计算误差界，补充了有限区间已有结果，适用于验证自动积分。
Stochastic Quadrature Rules for Solving PDEs using Neural Networks
本文针对神经网络求解PDE时的积分误差问题，提出在低维网格上使用高阶无偏随机求积规则，并为三角形和四面体单元设计新方法，证明其能以与蒙特卡洛相当的计算成本显著提升收敛速度，同时指出梯度精确积分是优化收敛的关键。
Fractional Quadrature rule and using its Exactness for the Müntz-Legendre Scaling Functions for Solving Fractional Differential Equations
针对传统求积法则计算分数幂函数积分存在误差的问题，本文提出可精确积分分数幂函数张成集内函数的分数求积法则，结合Müntz-Legendre尺度函数求解含Caputo导数的分数阶微分方程，经算例验证其精度优于Block-pulse方法。
Brushing up a theorem by Lehel Banjai on the convergence of Trapezoidal Rule Convolution Quadrature
本文研究了梯形法则卷积求积法在超几何问题中的收敛性，通过分析Lehel Banjai和Christian Lubich的文献，澄清了时间变量依赖性的估计。
This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize the Pythagorean eigenvalue theorem of Strang and Fix. The proposed blended quadrature rules have advantages over alternative integration rules for isogeometric analysis on uniform and non-uniform meshes as well as for different polynomial orders and continuity of the basis. The optimally-blended schemes improve the convergence rate of the method by two orde…
This work presents spectral, mesh-free, Green's theorem-based numerical quadrature schemes for integrating functions over planar regions bounded by rational parametric curves. Our algorithm proceeds in two steps: (1) We first find intermediate quadrature rules for line integrals along the region's boundary curves corresponding to Green's theorem. (2) We then use a high-order quadrature rule to compute the numerical antiderivative of the integrand along a coordinate axis, which is used to evaluate the Green's theorem line integral. We present two methods to compute the intermediate quadrature r…
Gaussian Quadratures with prescribed nodes via moment theory
本文利用矩理论解决了具有多个指定节点的最小高斯求积规则存在性问题，推广了 Blekherman 等人关于单个指定节点的已有结果。
Numerical Quadrature for Singular Integrals on Fractals
本研究针对自相似分形集上的正则与奇异积分，提出利用测度不变性将奇异积分转化为正则积分的复合求积规则，结合复合重心规则实现二阶收敛，可用于分形屏散射问题中奇异重积分的精确计算。
On Fast Implementation of Clenshaw-Curtis and Fejér-type Quadrature Rules
本文基于FFT、DCT和IDST快速计算Chebyshev点插值多项式系数，结合Oliver算法高效计算修正矩，提出Clenshaw-Curtis、Fejér第一和第二型规则的插值积分算法，适用于Jacobi权重乘以对数函数的函数积分，展示了其稳定性、精度及计算效率。
A MATLAB package computing simultaneous Gaussian quadrature rules for Multiple Orthogonal Polynomials
本文提出一个MATLAB程序包，利用新平衡程序降低Hessenberg特征值问题的条件数，从而在浮点算术中可靠计算多重正交多项式的同时高斯求积规则。
Quadrature as a least-squares and minimax problem
本文通过将插值求积公式的权重向量表示为超定线性系统的最小二乘解，并建立其与极小化极大解的关系，定义了求积规则的角度等参数以评估和比较不同规则。
Numerical weighted integration of functions having mixed smoothness
该研究针对混合光滑性加权Sobolev空间函数的$\u211d^d$加权积分逼近，推导了最优求积收敛速度的上下界，一维下得到精确收敛速度，高维下用阶梯双曲交叉节点的稀疏网格求积给出上界。
A framework is presented to compute approximations of an integral $I(f)=\displaystyle \int_a^b f(x) dx$ from a pair of companion rules and its associate rule. We show that an associate rule is a weighted mean of two companion rules. In particular, the trapezoidal (T) and Simpson (S) rules are weighted means of the companion pairs (L,R) and (T,M) respectively, with L the left rectangle, R the right rectangle and M the midpoint rules. As L,R,T and M reproduce exactly the number $π=\displaystyle \int_0^π2\, \sin^2(x) dx$, we named them the four "{beautiful}" \ rules. For this example the geometri…
Two quadrature rules for stochastic Itô-integrals with fractional Sobolev regularity
本文研究了具有分数Sobolev正则性的随机积分的数值正交问题，提出两种正交规则，分别适用于σ∈(0,1)和σ∈(1,2)的情况，并在L^p范数下具有σ阶收敛性。
Optimization approaches to quadrature: new characterizations of Gaussian quadrature on the line and quadrature with few nodes on plane algebraic curves, on the plane and in higher dimensions
本文研究了在平面代数曲线及高维空间中，利用少数节点进行求积的新方法，提出在有限条件下，存在精确度达2d-1次的求积规则，并展示了如何通过优化正定形式的值来构造高斯求积规则。
Error Bounds for the Numerical Integration of Functions with Limited Smoothness
本文基于经典求积理论，分析了Gauss和Clenshaw-Curtis求积公式在Legendre权重下，对有限光滑性被积函数的误差界，并证明了广泛求积公式对多种权重函数的适用性。
A Note on the Convergence of Symmetric Triangle Quadrature Rules
本文研究了对称三角形求积规则的收敛性，指出当多项式次数为偶数时，其收敛率更高，从而减少计算成本。
Deep Ritz Method with Adaptive Quadrature for Linear Elasticity
本文研究求解线性弹性方程的深度Ritz方法，引入基于$H^{1/2}(Γ_D)$范数的修正变分形式处理Dirichlet边界条件，证明其能量范数下的最佳逼近性，并提出基于自适应求积的数值积分技术以控制积分误差，有效提升了方法求解各类弹性问题的精度与效率。
Machine Learning Discovery of Optimal Quadrature Rules for Isogeometric Analysis
提出基于梯度下降和动态规划的机器学习策略，为等几何分析寻找最优求积规则，在保持精度的同时显著减少积分点数，实现1D至3D空间高达44%-82%的计算节省。
Beyond Tchakaloff Quadrature: Positive Functionals, Frames and Widths
本文拓展了Tchakaloff求积相关结论，引入严格$S$正性概念证明正可离散化的等价条件，推导了离散化问题的系列推论，给出求积宽度界并建立其与$D$最优设计的关联。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。