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41.
A. G. García J. M. Kim G. Pérez-Villalón 《Numerical Functional Analysis & Optimization》2013,34(1-2):126-144
Alising error arises whenever a sampling formula, valid for a prescribed space, is applied to a function in a bigger space. In this work, we estimate the aliasing error of classic and average sampling expansions in wavelet subspaces of a multiresolution analysis. 相似文献
42.
Let T be a Cowen-Douglas operator. In this paper, we study the von Neumann algebra V?(T) consisting of operators commuting with both T and T? from a geometric viewpoint. We identify operators in V?(T) with connection-preserving bundle maps on E(T), the holomorphic Hermitian vector bundle associated to T. By studying such bundle maps, the structure of V?(T) as well as information on reducing subspaces of T can be determined. 相似文献
43.
The evaluation of matrix functions of the form f(A)v, where A is a large sparse or structured symmetric matrix, f is a nonlinear function, and v is a vector, is frequently subdivided into two steps: first an orthonormal basis of an extended Krylov subspace of fairly small dimension is determined, and then a projection onto this subspace is evaluated by a method designed for small problems. This paper derives short recursion relations for orthonormal bases of extended Krylov subspaces of the type Km,mi+1(A)=span{A-m+1v,…,A-1v,v,Av,…,Amiv}, m=1,2,3,…, with i a positive integer, and describes applications to the evaluation of matrix functions and the computation of rational Gauss quadrature rules. 相似文献
44.
This paper introduces a robust preconditioner for general sparse matrices based on low‐rank approximations of the Schur complement in a Domain Decomposition framework. In this ‘Schur Low Rank’ preconditioning approach, the coefficient matrix is first decoupled by a graph partitioner, and then a low‐rank correction is exploited to compute an approximate inverse of the Schur complement associated with the interface unknowns. The method avoids explicit formation of the Schur complement. We show the feasibility of this strategy for a model problem and conduct a detailed spectral analysis for the relation between the low‐rank correction and the quality of the preconditioner. We first introduce the SLR preconditioner for symmetric positive definite matrices and symmetric indefinite matrices if the interface matrices are symmetric positive definite. Extensions to general symmetric indefinite matrices as well as to nonsymmetric matrices are also discussed. Numerical experiments on general matrices illustrate the robustness and efficiency of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
45.
46.
The Lanczos method with shift‐invert technique is exploited to approximate the symmetric positive semidefinite Toeplitz matrix exponential. The complexity is lowered by the Gohberg–Semencul formula and the fast Fourier transform. Application to the numerical solution of an integral equation is studied. Numerical experiments are carried out to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
47.
Jiansong Zhang Danping Yang Hongfei Fu Hui Guo 《Numerical Linear Algebra with Applications》2011,18(4):695-705
Based on the overlapping‐domain decomposition and parallel subspace correction method, a new parallel algorithm is established for solving time‐dependent convection–diffusion problem with characteristic finite element scheme. The algorithm is fully parallel. We analyze the convergence of this algorithm, and study the dependence of the convergent rate on the spacial mesh size, time increment, iteration times and sub‐domains overlapping degree. Both theoretical analysis and numerical results suggest that only one or two iterations are needed to reach to optimal accuracy at each time step. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
48.
It is well-known that Bi-CG can be adapted so that the operations withA
T can be avoided, and hybrid methods can be constructed in which it is attempted to further improve the convergence behaviour. Examples of this are CGS, Bi-CGSTAB, and the more general BiCGstab(l) method. In this paper it is shown that BiCGstab(l) can be implemented in different ways. Each of the suggested approaches has its own advantages and disadvantages. Our implementations allow for combinations of Bi-CG with arbitrary polynomial methods. The choice for a specific implementation can also be made for reasons of numerical stability. This aspect receives much attention. Various effects have been illustrated by numerical examples. 相似文献
49.
A. DowJ. Vermeer 《Topology and its Applications》1993,50(3):263-282
A characterization of compact subspaces of extremally disconnected spaces is given which is similar to Gleason's characterization that the extremally disconnected spaces are projective for the class of compact spaces. An equivalence is established between the questions of whether every basically disconnected space is embeddable into an extremally disconnected space and the Borel lifting problems for the category algebras of generalized Cantor cubes. We study an inductive method of strengthening the product topology on the Cantor cubes to extremally disconnected topologies and use this to establish, from CH, that every compact F-space of weight c+ embeds into an extremally disconnected space. 相似文献
50.
We study a semigroup of linear operators on a Banach space X which satisfies the condition codim X
0<, where
We show that X
0 is closed and establish some properties of the asymptotic behavior of the subspaces complementing X
0 to X. 相似文献