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Computing Eigenvalues And Eigenvectors Of A Dense Real Symmetric Matrix On The Ncube 6400
"... This report demonstrates parallel versions of the Eispack [Smith 76] functions TRED2 and TQL2 for finding all eigenvalues and eigenvectors of a dense, real symmetric matrix on the Ncube 6400. The real symmetric eigenvalue problem can be posed as follows: Given a real symmetric n \Theta n matrix A, c ..."
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Cited by 3 (0 self)
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This report demonstrates parallel versions of the Eispack [Smith 76] functions TRED2 and TQL2 for finding all eigenvalues and eigenvectors of a dense, real symmetric matrix on the Ncube 6400. The real symmetric eigenvalue problem can be posed as follows: Given a real symmetric n \Theta n matrix A
Semifragile Image authentication using realsymmetric matrix
 J. of Information Science and Engineering
"... In order to improve the detection of malicious tampering of images, it is necessary to decrease the fragility of hidden watermarks, even for digital images which have been distorted incidentally. In this paper, we propose a new semifragile digital watermarking technique based on eigenvalues and eig ..."
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Cited by 1 (1 self)
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and eigenvectors of real symmetric matrix generated by the pair of four pixels. A signature bit for detecting malicious tampering of an image is generated using the dominant eigenvector. The dominant eigenvalue can reduce the sensitivity of quantization based watermarking. The experimental results show
Geometric Invariant Semifragile Image Watermarking Using Real Symmetric Matrix
"... Abstract: In order to improve the detection of malicious tampering images, it is necessary to decrease the fragility of hidden watermarks, even for digital images which have been incidentally distorted. In this paper, we propose a new invariant semifragile digital watermarking technique based on e ..."
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Cited by 3 (0 self)
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on eigenvalues and eigenvectors of real symmetric matrix generated by the four pixel pairs. A signature bit for detecting the malicious tampering of an image is generated using the dominant eigenvector. And the multirings Zernike transform (MRZT) is proposed to achieve geometric invariance. The MRZT method
A periodic Jacobi matrix is a real symmetric matrix of the form
"... Abstract: The inverse eigenvalue problem for Hermitian matrices whose graph is a cycle is discussed. Some results concerning the multiplicities of eigenvalues of a ..."
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Abstract: The inverse eigenvalue problem for Hermitian matrices whose graph is a cycle is discussed. Some results concerning the multiplicities of eigenvalues of a
A Method for Fast Diagonalization of a 2x2 or 3x3 Real Symmetric Matrix
, 2014
"... A method is presented for fast diagonalization of a 2x2 or 3x3 real symmetric matrix, that is determination of its eigenvalues and eigenvectors. The Euler angles of the eigenvectors are computed. A small computer algebra program is used to compute some of the identities, and a C++ program for testin ..."
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A method is presented for fast diagonalization of a 2x2 or 3x3 real symmetric matrix, that is determination of its eigenvalues and eigenvectors. The Euler angles of the eigenvectors are computed. A small computer algebra program is used to compute some of the identities, and a C++ program
A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix
"... A program is presented for determining a few selected eigenvalues and their eigenvectors on either end of the spectrum of a large, real, symmetric matrix. Based on the Davidson method, which is extensively used in quantum chemistry/physics, the current implementation improves the power of the origin ..."
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Cited by 30 (9 self)
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A program is presented for determining a few selected eigenvalues and their eigenvectors on either end of the spectrum of a large, real, symmetric matrix. Based on the Davidson method, which is extensively used in quantum chemistry/physics, the current implementation improves the power
The University of Florida sparse matrix collection
 NA DIGEST
, 1997
"... The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural enginee ..."
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Cited by 536 (17 self)
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The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 775 (21 self)
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is contained in the socalled kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input spaceclassical model selection
Parallel Numerical Linear Algebra
, 1993
"... We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illust ..."
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Cited by 773 (23 self)
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illustrate these principles using current architectures and software systems, and by showing how one would implement matrix multiplication. Then, we present direct and iterative algorithms for solving linear systems of equations, linear least squares problems, the symmetric eigenvalue problem
Global Optimization with Polynomials and the Problem of Moments
 SIAM JOURNAL ON OPTIMIZATION
, 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear ma ..."
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Cited by 577 (48 self)
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We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear
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