共查询到20条相似文献,搜索用时 46 毫秒
1.
2.
无限广义块Toeplitz和Hankel矩阵求逆的统一方法 总被引:1,自引:0,他引:1
利用Sylvester位移方程的统一办法给出所谓的无限广义块Toeplitz和Hankel矩阵的求逆公式。 相似文献
3.
4.
5.
1、引言 各类对角占优矩阵是数值代数和矩阵分析研究中的重要课题之一.对于线性方程组AX=6,当系数矩阵A为(块)对角占优矩阵或广义(块)对角占优矩阵时,许多经典的迭代算法均是收敛的,同时对目前提出的一些修正算法也是收敛的.因此,判断一个矩阵是否是广义(块)对角占优矩阵具有重要意义.国内外许多学者都做了不少研究(见文[1.5]),本文给出了几个广义对角占优矩阵的判别方法. 相似文献
6.
行块矩阵M-P逆的充要条件 总被引:1,自引:1,他引:0
通过使用矩阵秩方法,证明了如下结果:[A,B]+=[αA+βB+]βAA*αBB*.[A,B][A,B]+=αAA++βBB+R(A)=R(B).这里,α+β=1,α>0,β>0.这两个结果是2007年田永革在国际线性代数学会会刊中获得的相应结果的推广. 相似文献
7.
8.
9.
10.
块H-矩阵与块矩阵的谱 总被引:1,自引:0,他引:1
利用G-函数概念研究块H-矩阵,引入若干块矩阵概念。获得了块H-矩阵的等价刻划,得到了一般块矩阵特征值的由G-函数描述的分布域,由于用G-函数刻划,所获结果具有一般性。 相似文献
11.
Fritzsche Bernd Kirstein Bernd Lasarow Andreas 《Integral Equations and Operator Theory》2004,48(3):305-330
We derive statements on rank invariance of Schwarz-Pick-Potapov
block matrices of matrix-valued Schur functions. The rank of these block
matrices coincides with the rank of some block matrices built from the corresponding
section matrices of Taylor coefficients. These results are applied to
the discussion of a matrix version of the classical Schur-Nevanlinna algorithm. 相似文献
12.
《数学物理学报(A辑)》2015,(5)
研究由Stieltjes函数生成的两类广义Loewner矩阵的秩不变性,证明了由同一Stieltjes函数生成的第一类同型的广义Loewner矩阵的秩是相等的,而生成的第二类同型的广义Loewner矩阵的秩相等或者相差1. 相似文献
13.
It is known [6] that for every function f in the generalized Schur class
and every nonempty open subset Ω of the unit disk
, there exist points z1,...,zn ∈Ω such that the n × nPick matrix
has κ negative eigenvalues. In this paper we discuss existence of an integer n0 such that any Pick matrix based on z1,...,zn ∈Ω with n ≥ n0 has κ negative eigenvalues. Definitely, the answer depends on Ω. We prove that if
, then such a number n0 does not exist unless f is a ratio of two finite Blaschke products; in the latter case the minimal value of n0 can be found. We show also that if the closure of Ω is contained in
then such a number n0 exists for every function f in
. 相似文献
14.
15.
16.
17.
18.
In the present paper we study the computation of the rank of a block bidiagonal Toeplitz (BBT) sequence of matrices. We propose matrix-based, numerical and symbolical, updating and direct methods, computing the rank of BBT matrices and comparing them with classical procedures. The methods deploy the special form of the BBT sequence, significantly reducing the required flops and leading to fast and efficient algorithms. The numerical implementation of the algorithms computes the numerical rank in contrast with the symbolical implementation, which guarantees the computation of the exact rank of the matrix. The combination of numerical and symbolical operations suggests a new approach in software mathematical computations denoted as hybrid computations. 相似文献
19.
20.
S. Serra 《BIT Numerical Mathematics》1999,39(1):152-175
It is well known that the generating function f L
1([–, ], ) of a class of Hermitian Toeplitz matrices A
n(f)
n
describes very precisely the spectrum of each matrix of the class. In this paper we consider n × n Hermitian block Toeplitz matrices with m × m blocks generated by a Hermitian matrix-valued generating function f L
1([–, ], C
m×m
). We extend to this case some classical results by Grenander and Szegö holding when m = 1 and we generalize the Toeplitz preconditioning technique introduced in the scalar case by R. H. Chan and F. Di Benedetto, G. Fiorentino and S. Serra. Finally, concerning the spectra of the preconditioned matrices, some asymptotic distribution properties are demonstrated and, in particular, a Szegö-style theorem is proved. A few numerical experiments performed at the end of the paper confirm the correctness of the theoretical analysis. 相似文献