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941.
Yu Chen 《Advances in Computational Mathematics》2002,16(2-3):175-190
The state-of-the-art, large-scale numerical simulations of the scattering problem for the Helmholtz equation in two dimensions rely on iterative solvers for the Lippmann–Schwinger integral equation, with an optimal CPU time O(m
3 log(m)) for an m-by-m wavelength problem. We present a method to solve the same problem directly, as opposed to iteratively, with the obvious advantage in efficiency for multiple right-hand sides corresponding to distinct incident waves. Analytically, this direct method is a hierarchical, recursive scheme consisting of the so-called splitting and merging processes. Algebraically, it amounts to a recursive matrix decomposition, for a cost of O(m
3), of the discretized Lippmann–Schwinger operator. With this matrix decomposition, each back substitution requires only O(m
2 log(m)); therefore, a scattering problem with m incident waves can be solved, altogether, in O(m
3 log(m)) flops. 相似文献
942.
本文对 Jordan标准形定理给出了一种使用初等变换的证明 ,直观意义明显、易于理解 ,可用于线性代数教学 . 相似文献
943.
Teruhiro Shirakura 《Annals of the Institute of Statistical Mathematics》1986,38(1):145-159
Summary For a given fractional 2
m
factorial (2
m
-FF) designT, the constitution of a block plan to divideT intok (2
r−1<k≦2
r
) blocks withr block factors each at two levels is proposed and investigated. The well-known three norms of the confounding matrix are used
as measures for determining a “good” block plan. Some theorems concerning the constitution of a block plan are derived for
a 2
m
-FF design of odd or even resolution. Two norms which may be preferred over the other norm are slightly modified. For each
value ofN assemblies with 11≦N≦26, optimum block plans fork=2 blocks with block sizes [N/2] andN−[N/2] minimizing the two norms are presented forA-optimal balanced 24-FF designs of resolutionV given by Srivastava and Chopra (Technometrics,13, 257–269). 相似文献
944.
Yingxin Jiang 《Fiber and Integrated Optics》2013,32(3):192-200
Abstract Through the modified transfer matrix method, the transmission properties of a one-dimensional coupled-resonator optical waveguide structure composed of metal layers and non-linear material layers is studied. Given proper incident frequency and structure parameters, an optical tri-stability has been achieved. The effect of loss has been considered. 相似文献
945.
In this paper, we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras and describe methods to construct tilting modules and tilting complexes inducing derived equivalences between them. 相似文献
946.
Matthew M. Lin 《Linear and Multilinear Algebra》2018,66(7):1279-1298
This work is to propose an iterative method of choice to compute a stable subspace of a regular matrix pencil. This approach is to define a sequence of matrix pencils via particular left null spaces. We show that this iteration preserves a semigroup property depending only on the initial matrix pencil. Via this recursion relationship, we propose an accelerated iterative method to compute the stable subspace and use it to provide a theoretical result to solve the principal square root of a given matrix, both nonsingular and singular. We show that this method can not only find out the matrix square root, but also construct an iterative approach which converges to the square root with any desired order. 相似文献
947.
M. Z. Abd-Alla H. A. Hassan H. A. Ayad 《Journal of Difference Equations and Applications》2018,24(8):1318-1345
This paper introduces sampling representations for discrete signals arising from self adjoint difference operators with mixed boundary conditions. The theory of linear operators on finite-dimensional inner product spaces is employed to study the second-order difference operators. We give necessary and sufficient conditions that make the operators self adjoint. The equivalence between the difference operator and a Hermitian Green's matrix is established. Sampling theorems are derived for discrete transforms associated with the difference operator. The results are exhibited via illustrative examples, involving sampling representations for the discrete Hartley transform. Families of discrete fractional Fourier-type transforms are introduced with an application to image encryption. 相似文献
948.
Integrable Couplings of the Boiti-Pempinelli-Tu Hierarchy and Their Hamiltonian Structures 下载免费PDF全文
Huiqun Zhang Yubin Zhou & Junqin Xu 《advances in applied mathematics and mechanics.》2016,8(4):588-598
Integrable couplings of the Boiti-Pempinelli-Tu hierarchy are constructed
by a class of non-semisimple block matrix loop algebras. Further, through using the
variational identity theory, the Hamiltonian structures of those integrable couplings
are obtained. The method can be applied to obtain other integrable hierarchies. 相似文献
949.
950.
Andrea Roccaverde 《Indagationes Mathematicae》2019,30(1):7-25
Breaking of ensemble equivalence between the microcanonical ensemble and the canonical ensemble may occur for random graphs whose size tends to infinity, and is signaled by a non-zero specific relative entropy between the two ensembles. In Garlaschelli et al. (2017) and Garlaschelli et al. (0000) it was shown that breaking occurs when the constraint is put on the degree sequence (configuration model). It is not known what is the effect on the relative entropy when the number of constraints is reduced, i.e., when only part of the nodes are constrained in their degree (and the remaining nodes are left unconstrained). Intuitively, the relative entropy is expected to decrease. However, this is not a trivial issue because when constraints are removed both the microcanonical ensemble and the canonical ensemble change. In this paper a formula for the relative entropy valid for generic discrete random structures, recently formulated by Squartini and Garlaschelli, is used to prove that the relative entropy is monotone in the number of constraints when the constraint is on the degrees of the nodes. It is further shown that the expression for the relative entropy corresponds, in the dense regime, to the degrees in the microcanonical ensemble being asymptotically multivariate Dirac and in the canonical ensemble being asymptotically Gaussian. 相似文献