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101.
应用矩阵块对角占优理论,讨论了块α-对角占优矩阵之间的蕴含关系,并得到了条件最弱的块严格α1-双对角占优的两个等价表征,并作为应用给出了块H矩阵新的判定准则,最后用数值例子说明结果的有效性. 相似文献
102.
一类特殊分块矩阵为循环矩阵的循环分块矩阵的几个性质 总被引:3,自引:0,他引:3
本文给出一类特殊分块矩阵为循环矩阵的循环分块矩阵的几个性质。 相似文献
103.
Jin Bai Kim 《数学研究及应用》1985,5(3):11-13
We give a characterization of a regular Boolean matrix and prove that AB = I Implies that BA = I, where A and B are Boolean matrices whose elements belong to a Boolean algebra of a set with more than two elements. 相似文献
104.
本文对满足条件AH=A>0,1/2(B+BH)≥0的矩阵A,B,建立了四个行列式不等式.某些著名的行列式不等式和一些已知结用,均可作为其推论. 相似文献
105.
Yurui Lin Linzhang Lu 《计算数学(英文版)》2007,25(5):553-560
In this paper, we present a useful result on the structures of circulant inverse Mmatrices. It is shown that if the n × n nonnegative circulant matrix A = Circ[c0, c1,… , c(n- 1)] is not a positive matrix and not equal to c0I, then A is an inverse M-matrix if and only if there exists a positive integer k, which is a proper factor of n, such that cjk 〉 0 for j=0,1…, [n-k/k], the other ci are zero and Circ[co, ck,… , c(n-k)] is an inverse M-matrix. The result is then extended to the so-called generalized circulant inverse M-matrices. 相似文献
106.
Motivated by the theory of self‐duality that provides a variational formulation and resolution for non‐self‐adjoint partial differential equations (Ann. Inst. Henri Poincaré (C) Anal Non Linéaire 2007; 24 :171–205; Selfdual Partial Differential Systems and Their Variational Principles. Springer: New York, 2008), we propose new templates for solving large non‐symmetric linear systems. The method consists of combining a new scheme that simultaneously preconditions and symmetrizes the problem, with various well‐known iterative methods for solving linear and symmetric problems. The approach seems to be efficient when dealing with certain ill‐conditioned, and highly non‐symmetric systems. The numerical and theoretical results are provided to show the efficiency of our approach. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
107.
A. Atrashchenko A. Nashchekin M. Mitrofanov V. P. Ulin V. P. Evtikhiev 《固体物理学:研究快报》2014,8(4):325-327
In this Letter, we have presented a new approach for the fabrication of nanowire media (wire metamaterials) by electrochemical methods. AIIIBV porous matrices (a host medium) were prepared by anodic electrochemical etching of industrial substrates. The host medium has been filled via electrochemical deposition with a metal and by means of annealing process. We have shown that this technique can be used to fabricate a nanowire medium with unique parameters (such as aspect ratio, high electric permittivity and strong χ(3) nonlinearity near the fundamental absorption edge of the host media). (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
108.
This paper shows that for unitary Hessenberg matrices the algorithm, with (an exceptional initial-value modification of) the Wilkinson shift, gives global convergence; moreover, the asymptotic rate of convergence is at least cubic, higher than that which can be shown to be quadratic only for Hermitian tridiagonal matrices, under no further assumption. A general mixed shift strategy with global convergence and cubic rates is also presented.
109.
The semi-infinite Toda lattice is the system of differential equations d
n
(t)/dt =
n
(t)(b
n+1(t) – b
n
(t)), db
n
(t)/dt = 2(
n
2(t) –
n–1
2(t)), n = 1, 2, ..., t > 0. The solution of this system (if it exists) is a pair of real sequences
n
(t), b
n
(t) which satisfy the conditions
n
(0) =
n
,, b
n
(0) = b
n
, where
n
> 0 and b
n
are given sequences of real numbers. It is well known that the system has a unique solution provided that both sequences
n
and b
n
are bounded. When at least one of the known sequences
n
and b
n
is unbounded, many difficulties arise and, to the best of our knowledge, there are few results concerning the solution of the system. In this letter we find a class of unbounded sequences
n
and b
n
such that the system has a unique solution. The results are illustrated with a typical example where the sequences
i
(t), b
i
(t), i = 1, 2, ... can be exactly determined. The connection of the Toda lattice with the semi-infinite differential-difference equation d2/dt
2 log h
n
= h
n+1 + h
n–1 – 2h
n
, n = 1, 2, ... is also discussed and the above results are translated to analogous results for the last equation. 相似文献
110.
For the unitary ensembles of N×N Hermitian matrices associated with a weight function w there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For the orthogonal and symplectic ensembles of Hermitian matrices there are 2×2 matrix kernels, usually constructed using skew-orthogonal polynomials, which play an analogous role. These matrix kernels are determined by their upper left-hand entries. We derive formulas expressing these entries in terms of the scalar kernel for the corresponding unitary ensembles. We also show that whenever w/w is a rational function the entries are equal to the scalar kernel plus some extra terms whose number equals the order of w/w. General formulas are obtained for these extra terms. We do not use skew-orthogonal polynomials in the derivations 相似文献