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1.
Sang-Gu Lee 《Linear algebra and its applications》2011,435(9):2097-2109
We investigate simultaneous solutions of the matrix Sylvester equations AiX-XBi=Ci,i=1,2,…,k, where {A1,…,Ak} and {B1,…,Bk} are k-tuples of commuting matrices of order m×m and p×p, respectively. We show that the matrix Sylvester equations have a unique solution X for every compatible k-tuple of m×p matrices {C1,…,Ck} if and only if the joint spectra σ(A1,…,Ak) and σ(B1,…,Bk) are disjoint. We discuss the connection between the simultaneous solutions of Sylvester equations and related questions about idempotent matrices separating disjoint subsets of the joint spectrum, spectral mapping for the differences of commuting k-tuples, and a characterization of the joint spectrum via simultaneous solutions of systems of linear equations. 相似文献
2.
Robert L. Ellis Israel Gohberg David C. Lay 《Integral Equations and Operator Theory》1995,22(4):375-419
This paper concerns a class of infinite block matrices that are analogous to finite block Toeplitz matrices. Also studied are corresponding matrix-valued functions that are orthogonal for a matrixvalued inner product. An appendix presents basic results on orthogonalization in a Hilbert module. 相似文献
3.
The implementation of implicit Runge-Kutta methods requires the solution of large systems of non-linear equations. Normally
these equations are solved by a modified Newton process, which can be very expensive for problems of high dimension. The recently
proposed triangularly implicit iteration methods for ODE-IVP solvers [5] substitute the Runge-Kutta matrixA in the Newton process for a triangular matrixT that approximatesA, hereby making the method suitable for parallel implementation. The matrixT is constructed according to a simple procedure, such that the stiff error components in the numerical solution are strongly
damped. In this paper we prove for a large class of Runge-Kutta methods that this procedure can be carried out and that the
diagnoal entries ofT are positive. This means that the linear systems that are to be solved have a non-singular matrix.
The research reported in this paper was supported by STW (Dutch Foundation for Technical Sciences). 相似文献
4.
5.
6.
In this paper are suggested new formulas for representation of matrices and their inverses in the form of sums of products of factor circulants, which are based on the analysis of the factor cyclic displacement of matrices. The results in applications to Toeplitz matrices generalized the Gohberg-Semencul, Ben-Artzi-Shalom and Heinig-Rost formulas and are useful for complexity analysis. 相似文献
7.
We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean. Some applications to matrix functions are also given. 相似文献
8.
Hugo J. Woerdeman 《Integral Equations and Operator Theory》1994,20(4):491-501
We construct the unique completion of a partial triangular matrix with compact operator entries that has the property that its sequence of singular values is minimal in lexicographical order among all completions. In addition some partial results regarding the singular values of this superoptimal completion are presented.The research was done while the author visited the Department of Mathematics at the George Washington University.Supported by the College of William and Mary 相似文献
9.
We give a matrix representation for the resolvent of the Friedrichs extension of some semibounded 2×2 operator matrices and study their essential spectrum. 相似文献
10.
For a comonic polynomialL() and a selfadjoint invertible matrixJ the following two factorization problems are considered: firstly, we parametrize all comonic polynomialsR() such that
. Secondly, if it exists, we give theJ-innerpseudo-outer factorizationL()=()R(), where () isJ-inner andR() is a comonic pseudo-outer polynomial. We shall also consider these problems with additional restrictions on the pole structure and/or zero structure ofR(). The analysis of these problems is based on the solution of a general inverse spectral problem for rational matrix functions, which consists of finding the set of rational matrix functions for which two given pairs are extensions of their pole and zero pair, respectively.The work of this author was supported by the USA-Israel Binational Science Foundation (BSF) Grant no. 9400271. 相似文献
11.
12.
A bi-infinite sequence ...,t
–2,t
–1,t
0,t
1,t
2,... of nonnegativep×p matrices defines a sequence of block Toeplitz matricesT
n
=(t
ik
),n=1,2,...,, wheret
ik
=t
k–i
,i,k=1,...,n. Under certain irreducibility assumptions, we show that the limit of the spectral radius ofT
n
, asn tends to infinity, is given by inf{()[0,]}, where () is the spectral radius of
jz
t
j
j
.Supported by SFB 343 Diskrete Strukturen in der Mathematik, Universität Bielefeld 相似文献
13.
Magdalena Wanat 《Linear algebra and its applications》2006,414(1):304-309
We generalize two results: Kraaijevanger’s 1991 characterization of diagonal stability via Hadamard products and the block matrix version of the closure of the positive definite matrices under Hadamard multiplication. We restate our generalizations in terms of Pα-matrices and α-scalar diagonally stable matrices. 相似文献
14.
S. R. Caradus 《Aequationes Mathematicae》1977,15(1):55-62
A bounded linear operatorT on Banach spaceX is called relatively regular if its nullspaceN(T) and rangeR(T) are closed complemented subspaces ofX. It is known that the product of two relatively regular operators is not necessarily relatively regular. This paper shows how to find conditions, more general than those previously known, to ensure that two relatively regular operators have relatively regular product.This work was supported in part by NRC Operating Grant A3985 and Canada Council Leave Fellowship. 相似文献
15.
Radu Teodorescu 《Integral Equations and Operator Theory》1998,32(2):234-241
In their paper [5], C. Foias and A. Frazho have found explicit formulas for the Schur contraction associated with a given contractive intertwining lifting. In this Note we give a more direct and probably the simplest way to find the Schur contraction for a given contractive intertwining lifting. 相似文献
16.
A partial matrix is a matrix where only some of the entries are given. We determine the maximum rank of the symmetric completions of a symmetric partial matrix where only the diagonal blocks are given and the minimum rank and the maximum rank of the antisymmetric completions of an antisymmetric partial matrix where only the diagonal blocks are given. 相似文献
17.
Mihály Bakonyi 《Integral Equations and Operator Theory》1992,15(2):173-185
H. Dym and I. Gohberg established in [6] necessary and sufficient conditions for the existence and uniqueness of an invertible block matrix F=(Fij)i,j=1,...,n such that Fij=Rij for |i–j|m and F–1 has a band triangular factorization and so (F–1)ij=0 for |i–j|>m. Here Rij, |i–j|m are given block matrices.The aim of this paper is to generalize these results in two directions. First, we shall allow Rij to be an (linear bounded) operator acting between the Hilbert spaces Hj and Hi. Secondly, the set of indices of the given Rij will be more general than banded ones. In fact, we will consider index sets which have an associated graph which is chordal. The case of partial positive operator matrices is also discussed. 相似文献
18.
In this paper we present an inertia result for Stein equations with
an indefinite right hand side. This result is applied to establish connnections
between the inertia of invertible hermitian block Toeplitz matrices and associated
orthogonal polynomials. 相似文献
19.
We shall discuss geometric properties of a quadrangle with parallelogramic properties in a convex cone of positive definite matrices with respect to Thompson metric. 相似文献
20.
Hari Bercovici 《Complex Analysis and Operator Theory》2007,1(3):335-339
Consider a domain
, and two analytic matrix-valued functions functions
. Consider also points
and positive integers n
1, n
2, . . . , n
N
. We are interested in the existence of an analytic function
such that X(ω) is invertible, and G(ω) coincides with X(ω)F(ω)X(ω)−1 up to order n
j
at the point ω
j
. We will see that such a function exists provided that F(ω
j
),G(ω
j
) have cyclic vectors, and the characteristic polynomials of F,G coincide up to order n
j
at ω
j
. This allows one to give a short proof to a result of Huang, Marcantognini and Young concerning spectral interpolation in
the unit disk.
The author was partially supported by a grant from the National Science Foundation.
Received: September 8, 2006. Accepted: January 11, 2007. 相似文献