共查询到20条相似文献,搜索用时 14 毫秒
1.
J. H. Brandts 《Numerical Linear Algebra with Applications》2002,9(3):249-261
In Matlab 6, there exists a command to generate a real Schur form, wheras another transforms a real Schur form into a complex one. There do not exist commands to prescribe the order in which the eigenvalues appear on the diagonal of the upper (quasi‐) triangular factor T. For the complex case, a routine is sketched in Golub and Van Loan (Matrix Computations (3rd edn). The John Hopkins University Press: Baltimore and London, 1996), that orders the diagonal of T according to their distance to a target value τ. In this technical note, we give a Matlab routine to sort real Schur forms in Matlab. It is based on a block‐swapping procedure by Bai and Demmel (Linear Algebra and Its Applications 1993; 186 : 73) We also describe how to compute a partial real Schur form (see Saad (Numerical methods for large eigenvalue problems. Manchester University Press: Manchester, 1992.)) in case the matrix A is very large. Sorting real Schur forms, both partially and completely, has important applications in the computation of real invariant subspaces. Copyright © 2002 by John Wiley & Sons, Ltd. 相似文献
2.
Skander Belhaj 《Numerical Algorithms》2008,47(1):15-34
In this paper, we consider an approximate block diagonalization algorithm of an n×n real Hankel matrix in which the successive transformation matrices are upper triangular Toeplitz matrices, and propose a
new fast approach to compute the factorization in O(n
2) operations. This method consists on using the revised Bini method (Lin et al., Theor Comp Sci 315: 511–523, 2004). To motivate our approach, we also propose an approximate factorization variant of the customary fast method based on Schur
complementation adapted to the n×n real Hankel matrix. All algorithms have been implemented in Matlab and numerical results are included to illustrate the effectiveness
of our approach. 相似文献
3.
Given m × n matrices A = [ajk ] and B = [bjk ], their Schur product is the m × n matrix A ○ B = [ajkbjk ]. For any matrix T, define ‖T‖ S = maxX ≠O ‖T ○ X ‖/‖X ‖ (where ‖·‖ denotes the usual matrix norm). For any complex (2n – 1)‐tuple μ = (μ –n +1, μ –n +2, …, μ n –1), let Tμ be the Hankel matrix [μ –n +j +k –1]j,k and define ??μ = {f ∈ L 1[–π, π] : f? (2j ) = μj for –n + 1 ≤ j ≤ n – 1} . It is known that ‖Tμ‖ S ≤ infequation/tex2gif-inf-18.gif ‖f ‖1. When equality holds, we say Tμ is distinguished. Suppose now that μ j ∈ ? for all j and hence that Tμ is hermitian. Then there is a real n × n hermitian unitary X and a real unit vector y such that 〈(Tμ ○ X )y, y 〉 = ‖Tμ ‖S . We call such a pair a norming pair for Tμ . In this paper, we study norming pairs for real Hankel matrices. Specifically, we characterize the pairs that norm some distinguished Schur multiplier Tμ . We do this by giving necessary and suf.cient conditions for (X, y ) to be a norming pair in the n ‐dimensional case. We then consider the 2‐ and 3‐dimensional cases and obtain further results. These include a new and simpler proof that all real 2 × 2 Hankel matrices are distinguished, and the identi.cation of new classes of 3 × 3 distinguished matrices. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
5.
Theory, algorithms and LAPACK-style software for computing a pair of deflating subspaces with specified eigenvalues of a regular matrix pair (A, B) and error bounds for computed quantities (eigenvalues and eigenspaces) are presented. Thereordering of specified eigenvalues is performed with a direct orthogonal transformation method with guaranteed numerical stability. Each swap of two adjacent diagonal blocks in the real generalized Schur form, where at least one of them corresponds to a complex conjugate pair of eigenvalues, involves solving a generalized Sylvester equation and the construction of two orthogonal transformation matrices from certain eigenspaces associated with the diagonal blocks. The swapping of two 1×1 blocks is performed using orthogonal (unitary) Givens rotations. Theerror bounds are based on estimates of condition numbers for eigenvalues and eigenspaces. The software computes reciprocal values of a condition number for an individual eigenvalue (or a cluster of eigenvalues), a condition number for an eigenvector (or eigenspace), and spectral projectors onto a selected cluster. By computing reciprocal values we avoid overflow. Changes in eigenvectors and eigenspaces are measured by their change in angle. The condition numbers yield bothasymptotic andglobal error bounds. The asymptotic bounds are only accurate for small perturbations (E, F) of (A, B), while the global bounds work for all (E, F.) up to a certain bound, whose size is determined by the conditioning of the problem. It is also shown how these upper bounds can be estimated. Fortran 77software that implements our algorithms for reordering eigenvalues, computing (left and right) deflating subspaces with specified eigenvalues and condition number estimation are presented. Computational experiments that illustrate the accuracy, efficiency and reliability of our software are also described. 相似文献
6.
Ion Armeanu 《代数通讯》2013,41(2):540-544
An ambivalent group is a finite group all of whose irreducible characters are real valued. By Brauer–Speiser theorem, if G is an ambivalent group, then the absolute Schur index m Q (χ) = m(χ) ≤2. In this note we shall prove that this property is true also for the derived subgroups of ambivalent groups. Also we will prove that there is a relation between the number of conjugacy classes of 2-regular cyclic subgroups of an ambivalent group and the irreducible characters with absolute Schur index 1. 相似文献
7.
Giuseppe Zampieri 《Journal d'Analyse Mathématique》1995,66(1):331-344
We prove the unicity of a complex of sheavesF whose microsupport is carried by a “dihedral” Lagrangian Λ ofT
* X (X=a real manifold) and which is simple with a prescribed shift at a regular point of Λ. Our method consists in reducing Λ,
by a real contact transformation, to the conormal bundle to aC
1-hypersuface, and then in using [K-S 1, Prop. 6.2.1] in the variant of [D'A-Z 1]. This is similar to [Z 2] but more general,
since complex contact transformations and calculations of shifts are not required. We then consider the case of a complex
manifoldX, and obtain some vanishing theorems for the complex of “microfunctions along Λ” similar to those of [A-G], [A-H], [K-S 1]
(cf. also [D'A-Z 3 5], [Z 2]). 相似文献
8.
A finite group G is called a Schur group, if any Schur ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. Recently, the authors have completely identified the cyclic Schur groups. In this article, it is shown that any abelian Schur group belongs to one of several explicitly given families only. In particular, any noncyclic abelian Schur group of odd order is isomorphic to ?3 × ?3 k or ?3 × ?3 × ? p where k ≥ 1 and p is a prime. In addition, we prove that ?2 × ?2 × ? p is a Schur group for every prime p. 相似文献
9.
The time complexity for testing whether an n-by-n real matrix is a P-matrix is reduced from O(2n
n
3) to O(2
n
) by applying recursively a criterion for P-matrices based on Schur complementation. A Matlab program implementing the associated algorithm is provided. 相似文献
10.
We determine the rank of a general real binary form of degree d?=?4 or d?=?5. In the case d?=?5, the possible values of the rank of such general forms are 3, 4, and 5. This is the first reported case, to our knowledge, where more than two typical ranks have been found. We prove that a real binary form of degree d with d real roots has rank?d. 相似文献
11.
Bin Zhu 《Journal of Algebraic Combinatorics》2008,27(1):35-54
We give a quiver representation theoretic interpretation of generalized cluster complexes defined by Fomin and Reading. Using
d-cluster categories defined by Keller as triangulated orbit categories of (bounded) derived categories of representations
of valued quivers, we define a d-compatibility degree (−∥−) on any pair of “colored” almost positive real Schur roots which generalizes previous definitions on the noncolored case
and call two such roots compatible, provided that their d-compatibility degree is zero. Associated to the root system Φ corresponding to the valued quiver, using this compatibility relation, we define a simplicial complex which has colored almost
positive real Schur roots as vertices and d-compatible subsets as simplices. If the valued quiver is an alternating quiver of a Dynkin diagram, then this complex is
the generalized cluster complex defined by Fomin and Reading.
Supported by the NSF of China (Grants 10471071) and by the Leverhulme Trust through the network ‘Algebras, Representations
and Applications’. 相似文献
12.
We deal with complex submanifolds in indefinite space forms. In particular, submanifolds with large index of relative nullity are emphasized. In that context, we prove cylinder theorems in terms of indefinite metrics. We also give a systematic way of constructing a family of new complete and closed indefinite complex submanifolds in the projective setting.In the appendix, we show that the method used for complex cases can be applied to real indefinite geometry. We prove real cylinder theorems including B-scrolls in the general signature. We also show two decomposition lemmas which clarify the relationships between the Hartman-Nirenberg cylinder theorem and slanted cylinder theorems in indefinite geometry. 相似文献
13.
Necessary conditions for Schur-positivity 总被引:1,自引:1,他引:0
Peter R. W. McNamara 《Journal of Algebraic Combinatorics》2008,28(4):495-507
In recent years, there has been considerable interest in showing that certain conditions on skew shapes A and B are sufficient for the difference s
A
−s
B
of their skew Schur functions to be Schur-positive. We determine necessary conditions for the difference to be Schur-positive. Specifically, we prove that if s
A
−s
B
is Schur-positive, then certain row overlap partitions for A are dominated by those for B. In fact, our necessary conditions require a weaker condition than the Schur-positivity of s
A
−s
B
; we require only that, when expanded in terms of Schur functions, the support of s
A
contains that of s
B
. In addition, we show that the row overlap condition is equivalent to a column overlap condition and to a condition on counts
of rectangles fitting inside A and B. Our necessary conditions are motivated by those of Reiner, Shaw and van Willigenburg that are necessary for s
A
=s
B
, and we deduce a strengthening of their result as a special case. 相似文献
14.
T. S. S. R. K. Rao 《Proceedings Mathematical Sciences》1997,107(1):35-42
In this paper we study a geometric property for Banach spaces called condition (*), introduced by de Reynaet al in [3], A Banach space has this property if for any weakly null sequencex
n of unit vectors inX, ifx
*
n
is any sequence of unit vectors inX
* that attain their norm at xn’s, then
. We show that a Banach space satisfies condition (*) for all equivalent norms iff the space has the Schur property. We also
study two related geometric conditions, one of which is useful in calculating the essential norm of an operator. 相似文献
15.
We introduce new expressions for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra under some conditions. We generalized some recent results for Drazin inverse and group inverse of complex matrices. 相似文献
16.
From the Real and Complex Coupled Dispersionless Equations to the Real and Complex Short Pulse Equations
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In the present paper, we study the real and complex coupled dispersionless (CD) equations, the real and complex short pulse (SP) equations geometrically and algebraically. From the geometric point of view, we first establish the link of the motions of space curves to the real and complex CD equations, then to the real and complex SP equations via hodograph transformations. The integrability of these equations are confirmed by constructing their Lax pairs geometrically. In the second part of the paper, it is made clear for the connection between the real and complex CD and SP equations and the two‐component extended Kadomtsew‐Petviashvili (KP) hierarchy. As a by‐product, the N‐soliton solutions in the form of determinants for these equations are provided. 相似文献
17.
The Schur convexity or concavity problem of the Gini mean values S(a, b; x, y) with respect to (x, y) ∈ (0, ∞) × (0, ∞) for fixed (a, b) ∈ R × R is still open. In this paper, we prove that S(a, b; x, y) is Schur convex with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b) : a 0, b 0, a + b 1}, and Schur concave with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b) : b 0, b a, a + b 1} ∪ {(a, b) : a 0, a b, a + b 1}. 相似文献
18.
In this article, we classify up to isomorphism the character tables of 2-generator p-groups of class two. 相似文献
19.
We give sufficient conditions which guarantee that the finite q-Hankel transforms have only real zeros which satisfy some asymptotic relations. The study is carried out using two different techniques. The first is by a use of Rouché's theorem and the other is by applying a theorem of Hurwitz and Biehler. In every study further restrictions are imposed on q(0,1). We compare the results via some interesting applications involving second and third q-Bessel functions as well as q-trigonometric functions. 相似文献
20.
Mustapha Raïssouli 《Linear and Multilinear Algebra》2019,67(2):213-220
Let T and S be two self-adjoint positive invertible operators of a complex Hilbert space H. In this paper, we investigate some inequalities involving the quadratic forms of the weighted arithmetic and harmonic means of T and S. Application for operator entropies is also discussed. 相似文献