共查询到20条相似文献,搜索用时 15 毫秒
1.
The Lyapunov method for determining the inertia of a matrix in terms of inertia of solutions of a certain linear matrix equation is extended to matrix polynomials.Generalization of well-known inertia theorems are obtained using the recently developed concept of Bezoutian for several matrix polynomials. 相似文献
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In this paper we obtain general infinite dimensional inertia theorems for linear pencils in Hilbert space which cover previously known results for the finite dimensional case and for block weighted shifts. Connections with definite subspaces for contractions in spaces with indefinite metric are discussed. 相似文献
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Kh. N. Narzullaev 《Journal of Mathematical Sciences》1984,25(2):1084-1089
One presents the proof of a theorem which gives the possibility to isolate DOTU matrices and allows us to use computers in the investigation of DOTU matrices of small size.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 159–166, 1981. 相似文献
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Yongzhong Song 《Numerische Mathematik》2002,92(3):563-591
Summary. This paper investigates the comparisons of asymptotic rates of convergence of two iteration matrices. On the basis of nonnegative
matrix theory, comparisons between two nonnegative splittings and between two parallel multisplitting methods are derived.
When the coefficient matrix A is Hermitian positive (semi)definite, comparison theorems about two P-regular splittings and
two parallel multisplitting methods are proved.
Received April 4, 1998 / Revised version received October 18, 1999 / Published online November 15, 2001 相似文献
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Ovidiu Carja 《Annali di Matematica Pura ed Applicata》1991,158(1):13-32
Summary We investigate some controllability properties of linear control systems in finite or infinite dimensions. 相似文献
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M. S. Derevyagin 《Mathematical Notes》2005,77(3-4):587-591
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Zhongli You JinRong Wang Donal O'Regan Yong Zhou 《Mathematical Methods in the Applied Sciences》2019,42(3):954-968
This paper investigates the relative controllability of delay differential systems with linear impulses and linear parts defined by permutable matrices. We use the impulsive delay Grammian matrix to discuss the relatively controllability of impulsive linear delay controlled systems and we use the Krasnoselskii's fixed point theorem to discuss the relatively controllability of impulsive semilinear delay controlled systems. Finally, two examples are presented to illustrate our theoretical results. 相似文献
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Kumar Anil; Joshi Mohan C.; Pani Amiya K. 《IMA Journal of Mathematical Control and Information》2007,24(1):115-136
** Email: anil{at}math.iitb.ac.in*** Email: mcj{at}math.iitb.ac.in**** Email: akp{at}math.iitb.ac.in In this paper, we consider the following control system governedby the non-linear parabolic differential equation of the form: [graphic: see PDF] where A is a linear operator with dense domain and f(t, y)is a non-linear function. We have proved that under Lipschitzcontinuity assumption on the non-linear function f(t, y), theset of admissible controls is non-empty. The optimal pair (u*,y*) is then obtained as the limit of the optimal pair sequence{(un*, yn*)}, where un* is a minimizer of the unconstrainedproblem involving a penalty function arising from the controllabilityconstraint and yn* is the solution of the parabolic non-linearsystem defined above. Subsequently, we give approximation theoremswhich guarantee the convergence of the numerical schemes tooptimal pair sequence. We also present numerical experimentwhich shows the applicability of our result. 相似文献
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Fernando C. Silva 《Linear and Multilinear Algebra》1995,40(2):95-102
Let A1and A2be matrices of sizes m×m and m×n, respectively. Suppose that some of the entries under the main diagonal of A1 are unknown and all the other entries of [A1 A2] are constant. We study the existence of a completely controllable completion of (A1,A2) and generalize a previous result on the same problem. 相似文献
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A partial Hermitian matrix is one in which some entries are specified and others are considered to be free (complex) variables. Assuming the undirected graph of the specified entries is chordal, it is shown that, with certain mild restrictions, a partial Hermitian matrix may be completed to a Hermitian matrix with any inertia allowed by the specified principal submatrices through the interlacing inequalities. This generalizes earlier work dealing with the existence of positive definite completions, and. as before, the chordality assumption is, in general, necessary. Further related observations dealing with Toeplitz completions and the minimum eigenvalues of completions are also made, and these raise additional questions. 相似文献
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Eric M. Rains 《Probability Theory and Related Fields》1998,112(3):411-423
Using the machinery of zonal polynomials, we examine the limiting behavior of random symmetric matrices invariant under conjugation
by orthogonal matrices as the dimension tends to infinity. In particular, we give sufficient conditions for the distribution
of a fixed submatrix to tend to a normal distribution. We also consider the problem of when the sequence of partial sums of
the diagonal elements tends to a Brownian motion. Using these results, we show that if O
n
is a uniform random n×n orthogonal matrix, then for any fixed k>0, the sequence of partial sums of the diagonal of O
k
n
tends to a Brownian motion as n→∞.
Received: 3 February 1998 / Revised version: 11 June 1998 相似文献
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We use the notion of triples D+ → H → D? of Hilbert spaces to develop an analog of the Friedrichs extension procedure for a class of nonsemibounded operator matrices. In addition, we suggest a general approach (stated in the same terms) to the construction of variational principles for the eigenvalues of such matrices. 相似文献
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This work is concerned with the relations between exact controllability and complete stabilizability for linear systems in Hilbert spaces. We give an affirmative answer to the open problem posed by Rabah and Karrakchou [R. Rabah, J. Karrakchou, Exact controllability and complete stabilizability for linear systems in Hilbert spaces, Appl. Math. Lett. 10 (1997) 35–40]. More precisely, if the -semigroup generated by is surjective and the pair with a bounded operator is completely stabilizable, then is exactly controllable without any additional condition. 相似文献