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991.
992.
993.
Yan Gu Wen Chen Chuan-Zeng Zhang 《International Journal of Solids and Structures》2011,48(18):2549-2556
This study documents the first attempt to apply the singular boundary method (SBM), a novel boundary only collocation method, to two-dimensional (2D) elasticity problems. Unlike the method of fundamental solutions (MFS), the source points coincide with the collocation points on the physical boundary by using an inverse interpolation technique to regularize the singularity of the fundamental solution of the equation governing the problems of interest. Three benchmark elasticity problems are tested to demonstrate the feasibility and accuracy of the proposed method through detailed comparisons with the MFS, boundary element method (BEM), and finite element method (FEM). 相似文献
994.
995.
For 0≤k≤n, let be the entries in Euler’s difference table and let . Dumont and Randrianarivony showed equals the number of permutations on [n] whose fixed points are contained in {1,2,…,k}. Rakotondrajao found a combinatorial interpretation of the number in terms of k-fixed-points-permutations of [n]. We show that for any n≥1, the sequence is essentially 2-log-concave and reverse ultra log-concave. 相似文献
996.
文章研究了一类函数增量的局部渐近性质,发现这类函数增量的局部渐近性对于一元实函数,二元及多元实函数,向量值函数和复函数在一定条件下都会保持不变,进而提出了两个相关的猜想:此类函数增量的渐近性是关于函数变换的拓扑不变量。 相似文献
997.
利用分析中的解析函数方法和代数中的矩阵方法,得到了m阶常系数齐次线性递推数列通项公式的解析表达式,是对已有结果的完善和推广. 相似文献
998.
Given an isotropic random vector X with log-concave density in Euclidean space
\mathbbRn{\mathbb{R}^n} , we study the concentration properties of |X| on all scales, both above and below its expectation. We show in particular that
l \mathbbP( | |X| - ?n | 3 t?n ) £ C exp ( -cn1/2 min(t3, t) ) "t 3 0, \begin{array}{l} \mathbb{P}\left ( \left | |X| - \sqrt{n} \right | \geq t\sqrt{n} \right ) \leq C \, {\rm exp} \left ( -cn^{1/2} {\rm min}(t^{3}, t) \right) \; \forall t \geq 0, \end{array} 相似文献
999.
We present a partial first-order affine-scaling method for solving smooth optimization with linear inequality constraints. At each iteration, the algorithm considers a subset of the constraints to reduce the complexity. We prove the global convergence of the algorithm for general smooth objective functions, and show it converges at sublinear rate when the objective function is quadratic. Numerical experiments indicate that our algorithm is efficient. 相似文献
1000.
Xian-Ming Gu Yong-Liang Zhao Xi-Le Zhao Bruno Carpentieri & Yu-Yun Huang 《高等学校计算数学学报(英文版)》2021,14(4):893-919
The $p$-step backward difference formula (BDF) for solving systems of
ODEs can be formulated as all-at-once linear systems that are solved by parallel-in-time preconditioned Krylov subspace solvers (see McDonald et al. [36] and Lin
and Ng [32]). However, when the BDF$p$ (2 ≤ $p$ ≤ 6) method is used to solve time-dependent PDEs, the generalization of these studies is not straightforward as $p$-step
BDF is not selfstarting for $p$ ≥ 2. In this note, we focus on the 2-step BDF which is
often superior to the trapezoidal rule for solving the Riesz fractional diffusion equations, and show that it results into an all-at-once discretized system that is a low-rank
perturbation of a block triangular Toeplitz system. We first give an estimation of the
condition number of the all-at-once systems and then, capitalizing on previous work,
we propose two block circulant (BC) preconditioners. Both the invertibility of these
two BC preconditioners and the eigenvalue distributions of preconditioned matrices
are discussed in details. An efficient implementation of these BC preconditioners is
also presented, including the fast computation of dense structured Jacobi matrices.
Finally, numerical experiments involving both the one- and two-dimensional Riesz
fractional diffusion equations are reported to support our theoretical findings. 相似文献
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