共查询到20条相似文献,搜索用时 15 毫秒
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2.
S. Börm 《Computing》2005,74(3):249-271
-matrices can be used to construct efficient approximations of discretized integral operators. The -matrix approximation can be constructed efficiently by interpolation, Taylor or multipole expansion of the integral kernel function, but the resulting representation requires a large amount of storage.In order to improve the efficiency, local Schur decompositions can be used to eliminate redundant functions from an original approximation, which leads to a significant reduction of storage requirements and algorithmic complexity. 相似文献
3.
Adaptive Low-Rank Approximation of Collocation Matrices 总被引:3,自引:2,他引:3
This article deals with the solution of integral equations using collocation methods with almost linear complexity. Methods
such as fast multipole, panel clustering and ℋ-matrix methods gain their efficiency from approximating the kernel function.
The proposed algorithm which uses the ℋ-matrix format, in contrast, is purely algebraic and relies on a small part of the
collocation matrix for its blockwise approximation by low-rank matrices. Furthermore, a new algorithm for matrix partitioning
that significantly reduces the number of blocks generated is presented.
Received August 15, 2002; revised September 20, 2002 Published online: March 6, 2003 相似文献
4.
Pawlak近似算子具有多种推广形式。讨论了完全分配格上的近似算子。通过近似空间中的不确定性映射,分别引入了三种形式的上近似算子及下近似算子,讨论了它们的基本性质及其与已有近似算子之间的关系。研究结果表明,目前文献中出现的多种近似算子可以作为完全分配格上近似算子的特例。 相似文献
5.
《Automatic Control, IEEE Transactions on》2008,53(7):1724-1730
6.
根据平面多项式曲线的等距有理参数化条件,构造了具有不同连续阶的OR插值曲线.由于OR曲线可通过恰当的参数变换产生有理形式的等距线,因此根据给定B啨zier曲线离散端点条件,可构造特定连续阶的OR样条曲线来逼近该Bézier曲线,而将OR样条曲线的精确等距线作为B啨zier曲线的逼近等距线. 相似文献
7.
David C. Del Rey Fernández Jason E. Hicken David W. Zingg 《Journal of scientific computing》2018,75(1):83-110
This paper is concerned with the accurate, conservative, and stable imposition of boundary conditions and inter-element coupling for multi-dimensional summation-by-parts (SBP) finite-difference operators. More precisely, the focus is on diagonal-norm SBP operators that are not based on tensor products and are applicable to unstructured grids composed of arbitrary elements. We show how penalty terms—simultaneous approximation terms (SATs)—can be adapted to discretizations based on multi-dimensional SBP operators to enforce boundary and interface conditions. A general SAT framework is presented that leads to conservative and stable discretizations of the variable-coefficient advection equation. This framework includes the case where there are no nodes on the boundary of the SBP element at which to apply penalties directly. This is an important generalization, because elements analogous to Legendre–Gauss collocation, i.e. without boundary nodes, typically have higher accuracy for the same number of degrees of freedom. Symmetric and upwind examples of the general SAT framework are created using a decomposition of the symmetric part of an SBP operator; these particular SATs enable the pointwise imposition of boundary and inter-element conditions. We illustrate the proposed SATs using triangular-element SBP operators with and without nodes that lie on the boundary. The accuracy, conservation, and stability properties of the resulting SBP–SAT discretizations are verified using linear advection problems with spatially varying divergence-free velocity fields. 相似文献
8.
粗糙集理论是一种处理不确定性问题的数学工具.粗糙近似算子是粗糙集理论中的核心概念,基于等价关系的Paw-lak粗糙近似算子可以推广为基于一般二元关系的广义粗糙近似算子.近似算子的拓扑结构是粗糙集理论的重点研究方向.文中主要研究基于一般二元关系的广义粗糙近似算子诱导拓扑的性质,给出了基于粒和基于子系统的广义粗糙近似算子诱... 相似文献
9.
With respect to a wavelet basis, singular integral operators can be well approximated by sparse matrices, and in Found. Comput. Math. 2: 203–245 (2002) and SIAM J. Math. Anal. 35: 1110–1132 (2004), this property was used to prove certain optimal complexity results in the context of adaptive wavelet
methods. These results, however, were based upon the assumption that, on average, each entry of the approximating sparse matrices
can be computed at unit cost. In this paper, we confirm this assumption by carefully distributing computational costs over
the matrix entries in combination with choosing efficient quadrature schemes. 相似文献
10.
An algorithm is presented that produces an integer vector nearly parallel to a given vector. The algorithm can be used to discover exact rational solutions of homogeneous or inhomogeneous linear systems of equations, given a sufficiently accurate approximate solution.As an application, we show how to verify rigorously the feasibility of degenerate vertices of a linear program with integer coefficients, and how to recognize rigorously certain redundant linear constraints in a given system of linear equations and inequalities. This is a first step towards the handling of degeneracies and redundandies within rigorous global optimization codes. 相似文献
11.
P. S. Malachivskyy Ya. V. Pizyur V. A. Andrunyk 《Cybernetics and Systems Analysis》2018,54(5):765-770
The authors establish the condition for the existence of the Chebyshev approximation by the sum of the polynomial and logarithmic expression with the least absolute error and Hermite interpolation at the end points of the interval. The method is proposed for determining the parameters of such Chebyshev approximation. 相似文献
12.
李兴宽 《计算机与数字工程》2013,41(8)
粗糙集的代数刻画是理论研究中最活跃的一个分支.论文将分子格中的预拓扑引入到粗集理论中,给出了由预拓扑导出的近似算子及其性质,讨论了近似算子与预拓扑之间的关系. 相似文献
13.
Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-variate Functions 总被引:3,自引:0,他引:3
The Kronecker tensor-product approximation combined with the
-matrix techniques provides an efficient tool to represent integral operators as well as certain functions F(A) of a discrete elliptic operator A in ℝ
d
with a high spatial dimension d. In particular, we approximate the functions A
−1 and sign(A) of a finite difference discretisation A∈ℝ
N
×
N
with a rather general location of the spectrum. The asymptotic complexity of our data-sparse representations can be estimated
by
(n
p
log
q
n), p = 1, 2, with q independent of d, where n=N
1/
d
is the dimension of the discrete problem in one space direction. In this paper (Part I), we discuss several methods of a separable approximation of multi-variate functions.
Such approximations provide the base for a tensor-product representation of operators. We discuss the asymptotically optimal
sinc quadratures and sinc interpolation methods as well as the best approximations by exponential sums. These tools will be applied in Part II continuing
this paper to the problems mentioned above. 相似文献
14.
This article is the second part continuing Part I [16]. We apply the
-matrix techniques combined with the Kronecker tensor-product approximation to represent integral operators as well as certain
functions F(A) of a discrete elliptic operator A in a hypercube (0,1)
d
∈ ℝ
d
in the case of a high spatial dimension d. We focus on the approximation of the operator-valued functions A
−
σ
, σ>0, and sign (A) for a class of finite difference discretisations A ∈ ℝ
N
×
N
. The asymptotic complexity of our data-sparse representations can be estimated by
(n
p
log
q
n), p = 1, 2, with q independent of d, where n=N
1/
d
is the dimension of the discrete problem in one space direction. 相似文献
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16.
Wei Lai Wang Xiaofeng Wu Aihua Zhou Rigui Zhu Changming 《Neural Processing Letters》2018,48(3):1671-1691
Neural Processing Letters - Low-rank representation (LRR) and its variants have been proved to be powerful tools for handling subspace segmentation problems. In this paper, we propose a new... 相似文献
17.
This paper is motivated by a special linear interpolation problem encountered in scan-line algorithms for scan-conversion of filled polygons. rounding-up integral linear interpolation is defined and its efficient computation is discussed. The paper then incorporates rounding-up integral linear interpolation into a scan-line algorithm for filled polygons, and it discusses the implementation of the algorithm. This approach has the advantage of only requiring integer arithmetic in the calculations. Furthermore, the approach provides a unified treatment for calculating span extrema for left and right edges of the polygon that guarantees the mutual exclusiveness of the ownership of boundary pixels of two filled polygons sharing an edge. 相似文献
18.
提出一种基于分段二次插值的单精度浮点数初等函数逼近设计,以实现倒数、均方根、均方根倒数、指数、三角函数等多种函数运算。通过对二次多项式进行变换,将1次平方运算、2次乘法运算和3次加法运算,转化为2次乘累加运算,并且采用复用乘累加结构的方法完成运算。实验结果证明,尽管整个逼近运算需要2个时钟周期完成,但是运算部分面积能够减少56%,总的硬件设计成本能够降低17.5%。 相似文献
19.
A unified fast time-stepping method for both fractional integral and derivative operators is proposed. The fractional operator is decomposed into a local part with memory length \(\varDelta T\) and a history part, where the local part is approximated by the direct convolution method and the history part is approximated by a fast memory-saving method. The fast method has \(O(n_0+\sum _{\ell }^L{q}_{\alpha }(N_{\ell }))\) active memory and \(O(n_0n_T+ (n_T-n_0)\sum _{\ell }^L{q}_{\alpha }(N_{\ell }))\) operations, where \(L=\log (n_T-n_0)\), \(n_0={\varDelta T}/\tau ,n_T=T/\tau \), \(\tau \) is the stepsize, T is the final time, and \({q}_{\alpha }{(N_{\ell })}\) is the number of quadrature points used in the truncated Laguerre–Gauss (LG) quadrature. The error bound of the present fast method is analyzed. It is shown that the error from the truncated LG quadrature is independent of the stepsize, and can be made arbitrarily small by choosing suitable parameters that are given explicitly. Numerical examples are presented to verify the effectiveness of the current fast method. 相似文献
20.
The class of -matrices allows an approximate matrix arithmetic with almost linear complexity. In the present paper, we apply the -matrix technique combined with the Kronecker tensor-product approximation (cf. [2, 20]) to represent the inverse of a discrete elliptic operator in a hypercube (0, 1)dd in the case of a high spatial dimension d. In this data-sparse format, we also represent the operator exponential, the fractional power of an elliptic operator as well as the solution operator of the matrix Lyapunov-Sylvester equation. The complexity of our approximations can be estimated by (dn log qn), where N=nd is the discrete problem size. 相似文献