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HERMITE MATRIX POLYNOMIALS AND SECOND ORDER MATRIX DIFFERENTIAL EQUATIONS 被引量:6
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作者 L.Jódar R.Company 《Analysis in Theory and Applications》 1996年第2期20-30,共11页
In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermit... In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermite matrix polynomials,the orthogonality property and a Rodrigues' formula are given. 展开更多
关键词 exp hermite matrix POLYNOMIALS AND SECOND ORDER matrix DIFFERENTIAL EQUATIONS
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THE UNIVERSAL UNITARY MATRIX AND UNIVERSAL HERMITE MATRIX
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作者 Yuan Huiping(Dept.of Math.,Yuzhou University,Chongqing 400033,PRC) 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2000年第S1期115-117,共3页
Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal(oblique)Hermi... Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal(oblique)Hermite matrix are studied further,and thismust be useful for matrix theory and applications(like optimization theory,symplecticgeometry and physics etc).In the paper,C<sup>m×n</sup>shows m×n compound matrix set,C<sub>n</sub><sup>m×n</sup>shows n step compound invertible matrix set,A<sup>*</sup> shows conjugate transpose matrix of A, 展开更多
关键词 MUST THE UNIVERSAL UNITARY matrix AND UNIVERSAL hermite matrix HP
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Volterra Integral Equation of Hermite Matrix Polynomials
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作者 Raed S. Batahan 《Analysis in Theory and Applications》 2013年第2期97-103,共7页
The primary purpose of this paper is to present the Volterra integral equa- tion of the two-variable Hermite matrix polynomials. Moreover, a new representation of these matrix polynomials are established here.
关键词 hermite matrix polynomials three terms recurrence relation and Volterra integralequation.
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ON HERMITE MATRIX POLYNOMIALS AND HERMITE MATRIX FUNCTIONS 被引量:1
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作者 LucasJodar EmilloDefez 《Analysis in Theory and Applications》 1998年第1期36-48,共0页
In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix ... In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix polynomials is proved. Asymptotic behaviour of Hermite matrix polynomials is studied and the relationship of Hermite matrix functions with certain matrix differential equations is developed. A new expression of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed. 展开更多
关键词 ON hermite matrix POLYNOMIALS AND hermite matrix FUNCTIONS
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SOLVABILITY OF A QUATERNION MATRIX EQUATION 被引量:2
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作者 Cao WenshengInstitute of Math.,Xiangtan Polytechnic Univ.,Xiangtan 411201,China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第4期490-498,共9页
This paper discusses the solvability of quaternion matrix equation A *X *B *±B X A=D and obtains it's general explicit solutions in terms of A,B,D and their Moore Penrose inverses.
关键词 Moore Penrose inverse quaternion matrix hermite matrix.
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Some Notes for Toeplitz Matrix 被引量:1
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作者 LIUShu-qiang ZHANGHe-ruing 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第3期286-291,共6页
In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz ... In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed. 展开更多
关键词 matrix Toeplitz matrix hermite matrix
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Generalization for Laplacian energy
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作者 LIU Jian-ping LIU Bo-lian 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2009年第4期443-450,共8页
Let G be a simple graph with n vertices and m edges. Let λ1, λ2,…, λn, be the adjacency spectrum of G, and let μ1, μ2,…, μn be the Laplacian spectrum of G. The energy of G is E(G) = n∑i=1|λi|, while the ... Let G be a simple graph with n vertices and m edges. Let λ1, λ2,…, λn, be the adjacency spectrum of G, and let μ1, μ2,…, μn be the Laplacian spectrum of G. The energy of G is E(G) = n∑i=1|λi|, while the Laplacian energy of G is defined as LE(G) = n∑i=1|μi-2m/n| Let γ1, γ2, ~ …, γn be the eigenvalues of Hermite matrix A. The energy of Hermite matrix as HE(A) = n∑i=1|γi-tr(A)/n| is defined and investigated in this paper. It is a natural generalization of E(G) and LE(G). Thus all properties about energy in unity can be handled by HE(A). 展开更多
关键词 energy (of matrix hermite matrix EIGENVALUE
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A convergence analysis of the inexact Rayleigh quotient iteration and simplified Jacobi-Davidson method for the large Hermitian matrix eigenproblem
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作者 JIA ZhongXiao WANG Zhen 《Science China Mathematics》 SCIE 2008年第12期2205-2216,共12页
The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, ... The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, it is shown in this paper that under the original given condition the inexact RQI may not quadratically converge to the desired eigenpair and even may misconverge to some other undesired eigenpair. A new condition, called the uniform positiveness condition, is given that can fix misconvergence problem and ensure the quadratic convergence of the inexact RQI. An alternative to the inexact RQI is the Jacobi-Davidson (JD) method without subspace acceleration. A new proof of its linear convergence is presented and a sharper bound is established in the paper. All the results are verified and analyzed by numerical experiments. 展开更多
关键词 eigenvalue EIGENVECTOR large hermite matrix INEXACT RQI simplified JD convergence misconvergence the uniform positiveness condition 65F15
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A Necessary and Sufficient Condition for Products of Quasi-Positive Definite Matrices and Generalization of Schur's Theorem
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作者 LI Chang xing (Department of Basic Courses, Xi’an Institute of Posts and Telecommunications, Xi’an 710061, P.R. China) 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2002年第3期53-56,69,共5页
A quasi positive definite matrix is the generalization of a positive definite matrix. A necessary and sufficient condition of quasi positive definite matrix is obtained in this paper for the Kronecker product and Ha... A quasi positive definite matrix is the generalization of a positive definite matrix. A necessary and sufficient condition of quasi positive definite matrix is obtained in this paper for the Kronecker product and Hadamard product of two quasi positive definite matrices, and Schur's achievements in Hadamard product of the positive definite matrix is generalized to quasi positive definite matrix theory. 展开更多
关键词 quasi positive definite matrix kronecker product hadamard product hermite matrix
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