共查询到20条相似文献,搜索用时 12 毫秒
1.
Reinhard Nabben 《Numerische Mathematik》1992,63(1):411-431
Summary We study block matricesA=[Aij], where every blockA
ij
k,k
is Hermitian andA
ii
is positive definite. We call such a matrix a generalized H-matrix if its block comparison matrix is a generalized M-matrix. These matrices arise in the numerical solution of Euler equations in fluid flow computations and in the study of invariant tori of dynamical systems. We discuss properties of these matrices and we give some equivalent conditions for a matrix to be a generalized H-matrix.Research supported by the Graduiertenkolleg mathematik der Universität Bielefeld 相似文献
2.
3.
Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations 总被引:3,自引:0,他引:3
Summary We discuss block matrices of the formA=[A
ij
], whereA
ij
is ak×k symmetric matrix,A
ij
is positive definite andA
ij
is negative semidefinite. These matrices are natural block-generalizations of Z-matrices and M-matrices. Matrices of this type arise in the numerical solution of Euler equations in fluid flow computations. We discuss properties of these matrices, in particular we prove convergence of block iterative methods for linear systems with such system matrices. 相似文献
4.
Computing Google’s PageRank via lumping the Google matrix was recently analyzed in [I.C.F. Ipsen, T.M. Selee, PageRank computation, with special attention to dangling nodes, SIAM J. Matrix Anal. Appl. 29 (2007) 1281–1296]. It was shown that all of the dangling nodes can be lumped into a single node and the PageRank could be obtained by applying the power method to the reduced matrix. Furthermore, the stochastic reduced matrix had the same nonzero eigenvalues as the full Google matrix and the power method applied to the reduced matrix had the same convergence rate as that of the power method applied to the full matrix. Therefore, a large amount of operations could be saved for computing the full PageRank vector. 相似文献
5.
The generalized eigenvalue problem with H a Hankel matrix and the corresponding shifted Hankel matrix occurs in number of applications such as the reconstruction of the shape of a polygon
from its moments, the determination of abscissa of quadrature formulas, of poles of Padé approximants, or of the unknown powers
of a sparse black box polynomial in computer algebra. In many of these applications, the entries of the Hankel matrix are
only known up to a certain precision. We study the sensitivity of the nonlinear application mapping the vector of Hankel entries
to its generalized eigenvalues. A basic tool in this study is a result on the condition number of Vandermonde matrices with
not necessarily real abscissas which are possibly row-scaled.
B. Beckermann was supported in part by INTAS research network NaCCA 03-51-6637.
G. H. Golub was supported in part by DOE grant DE-FC-02-01ER41177.
G. Labahn was supported in part by NSERC and MITACS Canada grants. 相似文献
6.
Vladimir Druskin 《Linear algebra and its applications》2008,429(7):1679-1683
We prove strictly monotonic error decrease in the Euclidian norm of the Krylov subspace approximation of exp(A)φ, where φ and A are respectively a vector and a symmetric matrix. In addition, we show that the norm of the approximate solution grows strictly monotonically with the subspace dimension. 相似文献
7.
Summary In this paper we investigate the set of eigenvalues of a perturbed matrix {ie509-1} whereA is given and n × n, ||< is arbitrary. We determine a lower bound for thisspectral value set which is exact for normal matricesA with well separated eigenvalues. We also investigate the behaviour of the spectral value set under similarity transformations. The results are then applied tostability radii which measure the distance of a matrixA from the set of matrices having at least one eigenvalue in a given closed instability domain b. 相似文献
8.
Yongzhong Song 《Numerische Mathematik》1993,65(1):245-252
Summary In a recent paper the author has proposed some theorems on the comparison of the asymptotic rates of convergence of two nonnegative splittings. They extended the corresponding result of Miller and Neumann and implied the earlier theorems of Varga, Beauwens, Csordas and Varga. An open question by Miller and Neumann, which additional and appropriate conditions should be imposed to obtain strict inequality, was also answered. This article continues to investigate the comparison theorems for nonnegative splittings. The new results extend and imply the known theorems by the author, Miller and Neumann.The Project Supported by the Natural Science Foundation of Jiangsu Province Education Commission 相似文献
9.
In the present paper, by extending the idea of conjugate gradient (CG) method, we construct an iterative method to solve the general coupled matrix equations
10.
We discuss the eigenvalue problem for general and structured matrix polynomials which may be singular and may have eigenvalues at infinity. We derive condensed forms that allow (partial) deflation of the infinite eigenvalue and singular structure of the matrix polynomial. The remaining reduced order staircase form leads to new types of linearizations which determine the finite eigenvalues and corresponding eigenvectors. The new linearizations also simplify the construction of structure preserving linearizations. 相似文献
11.
Matthew M. Lin 《Linear algebra and its applications》2010,433(3):681-689
The Euclidean distance matrix for n distinct points in Rr is generically of rank r + 2. It is shown in this paper via a geometric argument that its nonnegative rank for the case r = 1 is generically n. 相似文献
12.
Bo Cheng 《Linear algebra and its applications》2009,430(1):308-317
Let RM(n,d) be the class {A∣A is an n×n reducible nonnegative matrix and the greatest common divisor of the lengths of all cycles in D(A) is d}, where D(A) is the associated digraph of A. In this paper we determine the set of numbers of positive entries of A for A∈RM(n,d). We also characterize the reducible nonnegative matrices with the maximum and minimum numbers of positive entries. 相似文献
13.
Bruno Iannazzo 《Linear algebra and its applications》2011,434(1):174-184
We study the properties of palindromic quadratic matrix polynomials φ(z)=P+Qz+Pz2, i.e., quadratic polynomials where the coefficients P and Q are square matrices, and where the constant and the leading coefficients are equal. We show that, for suitable choices of the matrix coefficients P and Q, it is possible to characterize by means of φ(z) well known matrix functions, namely the matrix square root, the matrix polar factor, the matrix sign and the geometric mean of two matrices. Finally we provide some integral representations of these matrix functions. 相似文献
14.
Computing a function f(A) of an n-by-n matrix A is a frequently occurring problem in control theory and other applications. In this paper we introduce an effective approach for the determination of matrix function f(A). We propose a new technique which is based on the extension of Newton divided difference and the interpolation technique of Hermite and using the eigenvalues of the given matrix A. The new algorithm is tested on several problems to show the efficiency of the presented method. Finally, the application of this method in control theory is highlighted. 相似文献
15.
Ji-Guang Sun 《BIT Numerical Mathematics》1992,32(4):702-714
Componentwise perturbation bounds for the Cholesky,LDL
H
,QR andLU decompositions are derived. The bounds improve known results of the same type and reveal the structural characteristics of the perturbations.This subject was supported by the Institute of Information Processing of the University of Umeå and the Swedish Natural Science Research Council. 相似文献
16.
In this work, the sign distribution for all inverse elements of general tridiagonal H-matrices is presented. In addition, some computable upper and lower bounds for the entries of the inverses of diagonally dominant tridiagonal matrices are obtained. Based on the sign distribution, these bounds greatly improve some well-known results due to Ostrowski (1952) 23, Shivakumar and Ji (1996) 26, Nabben (1999) [21] and [22] and recently given by Peluso and Politi (2001) 24, Peluso and Popolizio (2008) 25 and so forth. It is also stated that the inverse of a general tridiagonal matrix may be described by 2n-2 parameters ( and ) instead of 2n+2 ones as given by El-Mikkawy (2004) 3, El-Mikkawy and Karawia (2006) 4 and Huang and McColl (1997) 10. According to these results, a new symbolic algorithm for finding the inverse of a tridiagonal matrix without imposing any restrictive conditions is presented, which improves some recent results. Finally, several applications to the preconditioning technology, the numerical solution of differential equations and the birth-death processes together with numerical tests are given. 相似文献
17.
In this paper we analyze the connections among different parametric settings in which the stability theory for linear inequality systems may be developed. Our discussion is focussed on the existence, or not, of an index set (possibly infinite). For some stability approaches it is not convenient to have a fixed set indexing the constraints. This is the case, for example, of discretization techniques viewed as approximation strategies (i.e., discretization regarded as data perturbation). The absence of a fixed index set is also a key point in the stability analysis of parametrized convex systems via standard linearization. In other frameworks the index set is very useful, for example if the constraints are perturbed one by one, even to measure the global perturbation size. This paper shows to what extent an index set may be introduced or removed in relation to stability. 相似文献
18.
By using generalized Riccati technique, linear positive functional and the weighted averages technique, some new oscillation criteria for self-adjoint Hamiltonian matrix system
(E) 相似文献
19.
In this paper, a generalization of a formula proposed by Van Loan [Computing integrals involving the matrix exponential, IEEE Trans. Automat. Control 23 (1978) 395–404] for the computation of multiple integrals of exponential matrices is introduced. In this way, the numerical evaluation of such integrals is reduced to the use of a conventional algorithm to compute matrix exponentials. The formula is applied for evaluating some kinds of integrals that frequently emerge in a number classical mathematical subjects in the framework of differential equations, numerical methods and control engineering applications. 相似文献
20.
The classical singular value decomposition for a matrix A∈Cm×n is a canonical form for A that also displays the eigenvalues of the Hermitian matrices AA∗ and A∗A. In this paper, we develop a corresponding decomposition for A that provides the Jordan canonical forms for the complex symmetric matrices and . More generally, we consider the matrix triple , where are invertible and either complex symmetric or complex skew-symmetric, and we provide a canonical form under transformations of the form , where X,Y are nonsingular. 相似文献