共查询到20条相似文献，搜索用时 15 毫秒
1.
Lyonell Boulton Peter Lancaster Panayiotis Psarrakos. 《Mathematics of Computation》2008,77(261):313-334
In the first part of this paper (Sections 2-4), the main concern is with the boundary of the pseudospectrum of a matrix polynomial and, particularly, with smoothness properties of the boundary. In the second part (Sections 5-6), results are obtained concerning the number of connected components of pseudospectra, as well as results concerning matrix polynomials with multiple eigenvalues, or the proximity to such polynomials.
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In this research article, we work with the notion of the measures of noncompactness in order to establish some results concerning the essential pseudospectra of closed, densely defined linear operators in the Banach space. We start by giving a refinement of the definition of the essential pseudospectra by means of the measure of noncompactness, and we give sufficient conditions on the perturbed operator to have its invariance. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(5):2031-2038
This paper is concerned with the stability of essential spectra of singular Sturm‐Liouville differential operators with complex‐valued coefficients. It is proved that the essential spectrum of the corresponding minimal operator is preserved by perturbations small at infinity with respect to the unperturbed operator. Based on it, 1‐dimensional Schrödinger operators under local dilative perturbations are studied. 相似文献
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讨论了一个随机选择修理工的可修复系统解的指数稳定性,首先通过对积分微分方程组描述的可修复系统生成的系统算子的本质谱的增长性约束和扰动后本质谱半径的变化情况进行分析,进而得到了可修复系统解的指数稳定性. 相似文献
5.
Aymen AMMAR Bilel BOUKETTAYA Aref JERIBI 《数学物理学报(B辑英文版)》2014,34(6):1922-1934
In the present paper, we define the S-left and the S-right essential spectra of a linear operator and we study the stability of the S-essential spectra on a Banach space. 相似文献
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This paper is devoted to the investigation of the essential approximate point spectrum and the essential defect spectrum of a 2 × 2 block operator matrix on a product of Banach spaces. The obtained results are applied to a two‐group transport operators with general boundary conditions in the Banach space Lp ([–a, a ] × [–1, 1]) × Lp ([–a, a ] × [–1, 1]), a > 0, p ≥ 1 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
Pseudospectra of rectangular matrices 总被引：1，自引：0，他引：1
Pseudospectra of rectangular matrices vary continuously withthe matrix entries, a feature that eigenvalues of these matricesdo not have. Some properties of eigenvalues and pseudospectraof rectangular matrices are explored, and an efficient algorithmfor the computation of pseudospectra is proposed. Applicationsare given in (square) eigenvalue computation (Lanczos iteration),square pseudospectra approximation (Arnoldi iteration), controltheory (nearest uncontrollable system) and game theory. 相似文献
8.
本文讨论了一类二维Fredholm方程的一种近拟解,通过利用二元函数的Taylor展开式,积分方程转化成一个关于未知函数及其相应的偏导数的线性代数方程组.数值例子表明了该方法的有效性. 相似文献
9.
A curve tracing algorithm for computing the pseudospectrum 总被引：2，自引：0，他引：2
Martin Brühl 《BIT Numerical Mathematics》1996,36(3):441-454
The boundary curve of the pseudospectrum of a matrix is defined as a contour line of its resolvent norm. A rather simple and efficient continuation method is presented, which determines the implicitly given curve by a prediction-correction scheme, where the correction step is accomplished by one single Newton step. Besides its efficiency the algorithm turns out to be very accurate as long as the boundary of the pseudospectrum is a smooth curve. Problems may arise at bifurcation points where the resolvent norm is not differentiable.This work was partially supported by Deutsche Forschungsgemeinschaft. 相似文献
10.
We study in this article a boundary‐value problem arising in the propagation of waves in an elastic half‐space covered by a layer with a vertical borehole. We first show a uniqueness theorem under some restrictions on the solution. For the existence, we use the direct integral equation method. We obtain a singular integral system on the half‐line. For the solvability, we reduce this system to an elliptic pseudodifferential equation and establish the Fredholm property. Finally, we compute the index of the associated operator for various values of Poisson's ratio. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
11.
Guixin Xu 《Linear and Multilinear Algebra》2018,66(12):2438-2467
This paper is concerned with the stability of essential spectra of self-adjoint relations under relatively compact perturbation in Hilbert spaces. Relationships between relative boundedness and relative compactness of linear relations are established, and some necessary and sufficient conditions of relative compactness and relative boundedness of linear relations are given. It is shown that the essential spectra of self-adjoint relations are invariant under either relatively compact perturbation or a more general perturbation. The results obtained in the present paper generalize the corresponding results for operators to relations, and some of which weaken certain assumptions of the related existing results. 相似文献
12.
Tian-zi Jiang 《计算数学(英文版)》1998,16(5):445-456
1.IntroductionQuantitativeprobabilisticanalysiswascarriedoutforseveralnumericalproblems.Forasystematicsurvey,werefertoTraubetal.(1988)andreferencestherein.Smale(1985)gavethefirstquantitativeanalysisforconcretemeasure.Heexpectedthattheapproachtheremightleadtoamoresystematicwayofanalysingforthecostofnumericalalgorithms.Heinrich(1991)continuedthislineandgavethefirstquantitativeanalysisforconcretemeasuresandalgorithmsforintegralequationofthesecondkind.There,theanalysiswascarriedoutfortheGalerkin… 相似文献
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Fernando Guevara Vasquez Benjamin Z. Webb 《Numerical Linear Algebra with Applications》2015,22(1):145-174
An isospectral matrix reduction is a procedure that reduces the size of a matrix while maintaining its eigenvalues up to a known set. As to not violate the fundamental theorem of algebra, the reduced matrices have rational functions as entries. Because isospectral reductions can preserve the spectrum of a matrix, they are fundamentally different from say the restriction of a matrix to an invariant subspace. We show that the notion of pseudospectrum can be extended to a wide class of matrices with rational function entries and that the pseudospectrum of such matrices shrinks with isospectral reductions. Hence, the eigenvalues of a reduced matrix are more robust to entry‐wise perturbations than the eigenvalues of the original matrix. Moreover, the isospectral reductions considered here are more general than those considered elsewhere. We also introduce the notion of an inverse pseudospectrum (or pseudoresonances), which indicates how stable the poles of a rational function valued matrix are to entry‐wise perturbations. Illustrations of these concepts are given for mass‐spring networks. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
16.
Computing the field of values and pseudospectra using the Lanczos method with continuation 总被引：1，自引：0，他引：1
The field of values and pseudospectra are useful tools for understanding the behaviour of various matrix processes. To compute these subsets of the complex plane it is necessary to estimate one or two eigenvalues of a large number of parametrized Hermitian matrices; these computations are prohibitively expensive for large, possibly sparse, matrices, if done by use of the QR algorithm. We describe an approach based on the Lanczos method with selective reorthogonalization and Chebyshev acceleration that, when combined with continuation and a shift and invert technique, enables efficient and reliable computation of the field of values and pseudospectra for large matrices. The idea of using the Lanczos method with continuation to compute pseudospectra is not new, but in experiments reported here our algorithm is faster and more accurate than existing algorithms of this type.This work was supported by Engineering and Physical Sciences Research Council grants GR/H/52139 and GR/H/94528. 相似文献
17.
Michael Taylor 《偏微分方程通讯》2017,42(8):1322-1334
We study a class of Toeplitz operators with discontinuous symbols, stimulated by classical work of Douglas and Widom. We extend the notion of a locally sectorial symbol from the setting of scalar Toeplitz operators on the circle to systems, acting on sections of vector bundles over a class of multidimensional domains with minimal smoothness, known as uniformly rectifiable domains, and establish Fredholm properties in this expanded setting. 相似文献
18.
V. R. Kostić Lj. Cvetković D. Lj. Cvetković 《Numerical Linear Algebra with Applications》2016,23(2):356-372
Usefulness of spectral localizations in analysis of various matrix properties, such as stability of dynamical systems, has led us to derive a pseudospectra localization technique using the ideas that come from diagonally dominant matrices. In such way, many theoretical and practical applications of pseudospectra (robust stability, transient behavior, nonnormal dynamics, etc.) can be linked with specific relationships between matrix entries. This allows one to understand certain phenomena that occur in practice better, as we show for the realistic model of soil energetic food web. The novelty of the presented results, therefore, lies not only in new mathematical formulations but also in the conceptual sense because it links stability with empirical data and their uncertainty limitations. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
19.
研究具有周期修复函数的机器人与其连带的安全装置构成的系统的可靠性.运用泛函分析的方法,特别是Banach空间上的线性算子半群C_0理论,证明了系统的适定性,并通过分析系统本质谱和经过扰动后半群的本质谱半径的变化,给出解的有限展开式。并进一步证明,0是系统的严格占优本征值,系统的非零本征值至多有两个,从而表明系统解以指数形式收敛. 相似文献
20.
给出一种求解第二类Fredholm和Volterra积分方程的数值算法,算法在数值积分技术的基础上使用Monte Carlo随机模拟方法求积分方程的近似解.通过数值例子证明了该算法是有效的. 相似文献