共查询到20条相似文献,搜索用时 62 毫秒
1.
M. Hasanov 《Mathematische Nachrichten》2006,279(8):843-853
The paper introduces a new class of two parameter non‐overdamped operator pencils arising from evolution equations. We investigate spectral properties, including variational principles for “interior” points of the spectrum. Examples leading to pencils of the new class are given. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
We study the eigenvalues of rank one perturbations of regular matrix pencils depending linearly on a complex parameter. We prove properties of the corresponding eigenvalue sets including a convergence result as the parameter tends to infinity and an eigenvalue interlacing property for real valued pencils having real eigenvalues only. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Qianglian Huang & Shuangyun Gao 《分析论及其应用》2012,28(2):146-155
Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvent of linear pencils in Banach spaces. Some practical criterions for the existence of generalized resolvents of the linear pencil λ→ T λ S are provided and an explicit expression of the generalized resolvent is also given. As applications, the characterization for the Moore-Penrose inverse of the linear pencil to be its generalized resolvent and the existence of the generalized resolvents of linear pencils of finite rank operators, Fredholm operators and semi-Fredholm operators are also considered. The results obtained in this paper extend and improve many results in this area. 相似文献
5.
Yu. Sh. Abramov 《Journal of Mathematical Sciences》1993,64(6):1278-1288
The variational properties of the spectra of a class of quadratic pencils are investigated. These operator pencils are not strongly damped, which is expressed in a considerable manner in its properties. The obtained results are fundamental in the investigation of two-parameter pencils of waveguide type, which model pencils arising in the theory of regular waveguides. The considerable difficulties, arising at the investigation of pencils of waveguide type, are explained by the fact that they do not generate Rayleigh systems in the entire space, but only on certain of its nonconvex homogeneous sets. These sets occur here as the sets of the admissible vectors of the corresponding extremal problems.Translated from Problemy Matematicheskogo Analiza, No. 11, pp. 80–96, 1990. 相似文献
6.
M.I. Gil' 《Journal of Mathematical Analysis and Applications》2008,338(2):1469-1476
We consider polynomial pencils whose coefficients are compact operators. Bounds for the sums of absolute values, real and imaginary parts of characteristic values are derived. Applications to differential and difference equations are discussed. 相似文献
7.
We study the convergence properties of an iterative method for a variational inequality defined on a solution set of the split common fixed point problem. The method involves Landweber-type operators related to the problem as well as their extrapolations in an almost cyclic way. The evaluation of these extrapolations does not require prior knowledge of the matrix norm. We prove the strong convergence under the assumption that the operators employed in the method are approximately shrinking. 相似文献
8.
We use some integral operators to establish a few special properties of absolute convergence systems for l
2. 相似文献
9.
Lorenzo Rosasco Silvia Villa Bằng Công Vũ 《Numerical Functional Analysis & Optimization》2017,38(5):602-626
In this article, we investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the stochastic extension to monotone inclusions of a proximal method studied in the literature for saddle point problems. It consists in a forward step determined by the stochastic evaluation of the cocoercive operator, a backward step in the dual variables involving the resolvent of the monotone operator, and an additional forward step using the stochastic evaluation of the cocoercive operator introduced in the first step. We prove weak almost sure convergence of the iterates by showing that the primal-dual sequence generated by the method is stochastic quasi-Fejér-monotone with respect to the set of zeros of the considered primal and dual inclusions. Additional results on ergodic convergence in expectation are considered for the special case of saddle point models. 相似文献
10.
本文讨论了一类在弦和梁的微小振动中出现的二次算子族L(λ)=λ~2MλK-A的谱分布问题,进而将所得结论与无穷维Hamilton算子联系起来,利用无穷维Hamilton算子的特殊结构,得到了一类非负无穷维Hamilton算子的谱分布,这为无穷维Hamilton算子的半群方法提供了理论保证. 相似文献
11.
Sergey A. Denisov 《Journal of Functional Analysis》2008,254(8):2186-2226
For a large class of Schrödinger operators, we introduce the hyperbolic quadratic pencils by making the coupling constant dependent on the energy in the very special way. For these pencils, many problems of scattering theory are significantly easier to study. Then, we give some applications to the original Schrödinger operators including one-dimensional Schrödinger operators with L2-operator-valued potentials, multidimensional Schrödinger operators with slowly decaying potentials. 相似文献
12.
A classical Rayleigh-quotient iterative algorithm (known as “broken iteration”) for finding eigenvalues and eigenvectors is
applied to semisimple regular matrix pencils A − λB. It is proved that cubic convergence is attained for eigenvalues and superlinear convergence of order three for eigenvectors.
Also, each eigenvalue has a local basin of attraction. A closely related Newton algorithm is examined. Numerical examples
are included.
Dedicated to the memory of Gene H. Golub. 相似文献
13.
研究含参数$l$非方矩阵对广义特征值极小扰动问题所导出的一类复乘积流形约束矩阵最小二乘问题.与已有工作不同,本文直接针对复问题模型,结合复乘积流形的几何性质和欧式空间上的改进Fletcher-Reeves共轭梯度法,设计一类适用于问题模型的黎曼非线性共轭梯度求解算法,并给出全局收敛性分析.数值实验和数值比较表明该算法比参数$l=1$的已有算法收敛速度更快,与参数$l=n$的已有算法能得到相同精度的解.与部分其它流形优化相比与已有的黎曼Dai非线性共轭梯度法具有相当的迭代效率,与黎曼二阶算法相比单步迭代成本较低、总体迭代时间较少,与部分非流形优化算法相比在迭代效率上有明显优势. 相似文献
14.
Principal lattices are distributions of points in the plane obtained from a triangle by drawing equidistant parallel lines
to the sides and taking the intersection points as nodes. Interpolation on principal lattices leads to particularly simple
formulae. These sets were generalized by Lee and Phillips considering three-pencil lattices, generated by three linear pencils.
Inspired by the addition of points on cubic curves and using duality, we introduce an addition of lines as a way of constructing
lattices generated by cubic pencils. They include three-pencil lattices and then principal lattices. Interpolation on lattices
generated by cubic pencils has the same good properties and simple formulae as on principal lattices.
Dedicated to C.A. Micchelli for his mathematical contributions and friendship on occasion of his sixtieth birthday
Mathematics subject classifications (2000) 41A05, 41A63, 65D05.
J.M. Carnicer: Partially supported by the Spanish Research Grant BFM2003-03510, by Gobierno de Aragón and Fondo Social Europeo. 相似文献
15.
B. M. Podlevskii 《Journal of Mathematical Sciences》1996,79(6):1397-1401
We study the generalized eigenvalue problem for a uniformly hyperbolic or totally hyperbolic polynomial operator pencil of
arbitrary order. In the context of the variational approach to the problem of determining the eigenvalues of such pencils
we propose and justify a recursive algorithm for finding an eigenpair. To accelerate the convergence we propose using the
Rayleigh-Ritz procedure. We give data from a numerical implementation of the algorithm.
Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 24–28. 相似文献
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Hongguo Xu 《Linear algebra and its applications》2006,414(1):97-124
We study two matrix pencils that arise, respectively, in discrete-time and continuous-time optimal and robust control. We introduce a one-to-one transformation between these two pencils. We show that for the pencils under the transformation, their regularity is preserved and their eigenvalues and deflating subspaces are equivalently related. The eigen-structures of the pencils under consideration have strong connections with the associated control problems. Our result may be applied to connect the discrete-time and continuous-time control problems and eventually lead to a unified treatment of these two types of control problems. 相似文献
18.
Hakki İsmail Erdogan 《Journal of Geometry》1990,38(1-2):39-41
In this work,it is shown that n pencils of spheres which belong to the same bundle form a hexagonal-surface-web.Firstly,4 pencils of spheres orthogonal to the same sphere are taken into consideration. Later,by means of a suitable transformation,the equations of these 4 pencils of spheres are written in their simplest form and the equation of the surface web is obtained.Then,it is concluded that any 4- pencils of spheres belonging to the same bundle form a hexagonal-surface-web.From this we conclude that a surface n-web which is formed by n pencils of spheres belonging to the same bundle is a hexagonal web.n pencils of spheres are said to belong to the same bundle,if all the spheres cut a fixed sphere orthogonally. 相似文献
19.
《Chaos, solitons, and fractals》2001,12(12):2127-2142
The issue of dimensionality and signature of the observed universe is analysed. Neither of the two properties follows from first principles of physics, save for a remarkably fruitful Cantorian fractal spacetime approach pursued by El Naschie, Nottale and Ord. In the present paper, the author's theory of pencil-generated spacetime(s) is invoked to provide a clue. This theory identifies spatial coordinates with pencils of lines and the time dimension with a specific pencil of conics. Already its primitive form, where all pencils lie in one and the same projective plane, implies an intricate connection between the observed multiplicity of spatial coordinates and the (very) existence of the arrow of time. A qualitatively new insight into the matter is acquired, if these pencils are not constrained to be coplanar and are identified with the pencils of fundamental elements of a Cremona transformation in a projective space. The correct dimensionality of space (3) and time (1) is found to be uniquely tied to the so-called quadro-cubic Cremona transformations – the simplest non-trivial, non-symmetrical Cremona transformations in a projective space of three dimensions. Moreover, these transformations also uniquely specify the type of a pencil of fundamental conics, i.e. the global structure of the time dimension. Some physical and psychological implications of these findings are mentioned, and a relationship with the Cantorian model is briefly discussed. 相似文献
20.
Jos L. M. Van Dorsselaer 《BIT Numerical Mathematics》1997,37(4):833-845
The concept of ε-pseudospectra for matrices, introduced by Trefethen and his coworkers, has been studied extensively since
1990. In this paper, ε-pseudospectra for matrix pencils, which are relevant in connection with generalized eigenvalue problems,
are considered. Some properties as well as the practical computation of ε-pseudospectra for matrix pencils will be discussed.
As an application, we demonstrate how this concept can be used for investigating the asymptotic stability of stationary solutions
to time-dependent ordinary or partial differential equations; two cases, based on Burgers' equation, will be shown.
This research has been supported by the Netherlands Organization for Scientific Research (N.W.O.) 相似文献