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3,431
Zero asymptotic behaviour for orthogonal matrix polynomials
 MR 2000J:42037 ZBL 0945.42013
, 1999
"... Weakstar asymptotic results are obtained for the zeros of orthogonal matrix polynomials (i.e. the zeros of their determinants) on R from two different assumptions: first from the convergence of matrix coefficients occurring in the threeterm recurrence for these polynomials and, second, from some c ..."
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Cited by 4 (0 self)
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Weakstar asymptotic results are obtained for the zeros of orthogonal matrix polynomials (i.e. the zeros of their determinants) on R from two different assumptions: first from the convergence of matrix coefficients occurring in the threeterm recurrence for these polynomials and, second, from some
An Orthogonal Matrix Optimization by Dual Cayley Parametrization Technique
 4TH INTERNATIONAL SYMPOSIUM ON INDEPENDENT COMPONENT ANALYSIS AND BLIND SIGNAL SEPARATION (ICA2003
, 2003
"... This paper addresses a mathematically sound technique for the orthogonal matrix optimization problem that has broad applications in recent signal processing problems including the independent component analysis. We propose Dual Cayley parametrization technique that can decompose a slightly restricte ..."
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Cited by 7 (0 self)
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This paper addresses a mathematically sound technique for the orthogonal matrix optimization problem that has broad applications in recent signal processing problems including the independent component analysis. We propose Dual Cayley parametrization technique that can decompose a slightly
Orthogonal matrix polynomials and higher order recurrence relations
, 1993
"... It is wellknown that orthogonal polynomials on the real line satisfy a threeterm recurrence relation and conversely every system of polynomials satisfying a threeterm recurrence relation is orthogonal with respect to some positive Borel measure on the real line. In this paper we extend this res ..."
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Cited by 57 (9 self)
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this result and show that every system of polynomials satisfying some (2N + 1)term recurrence relation can be expressed in terms of orthonormal matrix polynomials for which the coefficients are N × N matrices. We apply this result to polynomials orthogonal with respect to a discrete Sobolev inner product
Superposition Formulas for PseudoOrthogonal Matrix Riccati Equations
"... The purpose of this article is to derive superposition formulas for pseudoorthogonal matrix Riccati equations of even dimensions N 4. The superposition formulas will be written in closed form in terms of ve particular solutions for N 8 and six for N 6. The importance of pseudoorthogonal matrix R ..."
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The purpose of this article is to derive superposition formulas for pseudoorthogonal matrix Riccati equations of even dimensions N 4. The superposition formulas will be written in closed form in terms of ve particular solutions for N 8 and six for N 6. The importance of pseudoorthogonal matrix
Further Properties of Random Orthogonal Matrix Simulation
"... doi:10.1016/j.matcom.2012.07.013. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before i ..."
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doi:10.1016/j.matcom.2012.07.013. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Page 1 of 37 Ac ce pte d M an us cri pt
Simple LU and QR based nonorthogonal matrix joint diagonalization
 of Lecture Notes in Computer Science
, 2006
"... Abstract. A class of simple Jacobitype algorithms for nonorthogonal matrix joint diagonalization based on the LU or QR factorization is introduced. By appropriate parametrization of the underlying manifolds, i.e. using triangular and orthogonal Jacobi matrices we replace a high dimensional minimiz ..."
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Cited by 8 (2 self)
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Abstract. A class of simple Jacobitype algorithms for nonorthogonal matrix joint diagonalization based on the LU or QR factorization is introduced. By appropriate parametrization of the underlying manifolds, i.e. using triangular and orthogonal Jacobi matrices we replace a high dimensional
Factored orthogonal matrixvector multiplication with applications to parallel and adaptive eigenfiltering and SVD
, 1994
"... A novel algorithm is presented for adaptive eigenfiltering and for updating the singular value decomposition (SVD). It is an improvement upon an earlier developed Jacobitype SVD updating algorithm, where now the exact orthogonality of the matrix of singular vectors/eigenvectors is guaranteed by sto ..."
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Cited by 1 (1 self)
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A novel algorithm is presented for adaptive eigenfiltering and for updating the singular value decomposition (SVD). It is an improvement upon an earlier developed Jacobitype SVD updating algorithm, where now the exact orthogonality of the matrix of singular vectors/eigenvectors is guaranteed
Orthogonal matrix polynomials, scalar type Rodrigues’ formulas and Pearson equations
 J. Approx. Theory
"... Some families of orthogonal matrix polynomials satisfying second order differential equations with coefficients independent of n have recently been introduced (see [DG1]). An important difference with the scalar classical families of Jacobi, Laguerre and Hermite, is that these matrix families do not ..."
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Cited by 8 (1 self)
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Some families of orthogonal matrix polynomials satisfying second order differential equations with coefficients independent of n have recently been introduced (see [DG1]). An important difference with the scalar classical families of Jacobi, Laguerre and Hermite, is that these matrix families do
Indexing by latent semantic analysis
 JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE
, 1990
"... A new method for automatic indexing and retrieval is described. The approach is to take advantage of implicit higherorder structure in the association of terms with documents (“semantic structure”) in order to improve the detection of relevant documents on the basis of terms found in queries. The p ..."
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Cited by 3779 (35 self)
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. The particular technique used is singularvalue decomposition, in which a large term by document matrix is decomposed into a set of ca. 100 orthogonal factors from which the original matrix can be approximated by linear combination. Documents are represented by ca. 100 item vectors of factor weights. Queries
Results 11  20
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3,431