This paper presents that the consistency test with consideration of a tolerance deviation in fuzzy AHP proposed by L. C. Leung and D. Cao (2000) is not efficient and has some errors, hence a new method of fuzzy consis...
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This paper presents that the consistency test with consideration of a tolerance deviation in fuzzy AHP proposed by L. C. Leung and D. Cao (2000) is not efficient and has some errors, hence a new method of fuzzy consistency test by direct fuzzification of (Quick Response) qr algorithm - which is one of numerical methods for calculating eigenvalues of an arbitrary matrix - has been proposed.
A new fast algorithm for computing the zeros of a polynomial in O(n(2)) time using O(n) memory is developed. The eigenvalues of the Frobenius companion matrix are computed by applying a nonunitary analogue of Francis&...
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A new fast algorithm for computing the zeros of a polynomial in O(n(2)) time using O(n) memory is developed. The eigenvalues of the Frobenius companion matrix are computed by applying a nonunitary analogue of Francis's implicitly shifted qr algorithm to a factored form of the matrix. The algorithm achieves high speed and low memory use by preserving the factored form. It also provides a residual and an error estimate for each root. Numerical tests confirm the high speed of the algorithm.
Driessel [K.R. Driessel, Computing canonical forms using flows, Linear Algebra Appl. 379 (2004) 353379] introduced the notion of quasi-projection onto the range of a linear transformation from one inner product space ...
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Driessel [K.R. Driessel, Computing canonical forms using flows, Linear Algebra Appl. 379 (2004) 353379] introduced the notion of quasi-projection onto the range of a linear transformation from one inner product space into another inner product space. Here we introduce the notion of quasi-projection onto the intersection of the ranges of two linear transformations from two inner product spaces into a third inner product space. As an application, we design a new family of iso-spectral flows on the space of symmetric matrices that preserves zero patterns. We discuss the equilibrium points of these flows. We conjecture that these flows generically converge to diagonal matrices. We perform some numerical experiments with these flows which support this conjecture. We also compare our zero-preserving flows with the Toda flow. (c) 2006 Elsevier Inc. All rights reserved.
We present a numerical method for computing the SVD-like decomposition B = QDS(-1), where Q is orthogonal, S is symplectic, and D is a permuted diagonal matrix. The method can be applied directly to compute the canoni...
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We present a numerical method for computing the SVD-like decomposition B = QDS(-1), where Q is orthogonal, S is symplectic, and D is a permuted diagonal matrix. The method can be applied directly to compute the canonical form of the Hamiltonian matrices of the form JB(T)B, where J = [(-I 0) (0 I)]. It can also be applied to solve the related application problems such as the gyroscopic systems and linear Hamiltonian systems. Error analysis and numerical examples show that the eigenvalues of JB(T)B computed by this method are more accurate than those computed by the methods working on the explicit product JB(T)B or BJB(T)
The research paper introduces an advanced asymmetric biometric image encryption technique that integrates Quasi-Zernike synthesis (QZS), qr algorithm, and hybrid transforms for enhanced security and integrity. The enc...
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The research paper introduces an advanced asymmetric biometric image encryption technique that integrates Quasi-Zernike synthesis (QZS), qr algorithm, and hybrid transforms for enhanced security and integrity. The encryption process incorporates qr decomposition, generating an orthogonal matrix Q that adds obfuscation and randomness to the image representation. qr is also resilient to attacks that exploit vulnerabilities in PTFT-based cryptosystems. QZS further improves security by capturing spatial information and complex features. The use of the compressed sparse row (CSR) format enables efficient storage and secure transmission. This integration provides a robust solution for confidential, secure image communication, applicable in military, surveillance, and sensitive data transfer scenarios. Moreover, watermarking ensures protection from unauthorized access, strengthening security measures. Experimental evaluations demonstrate the proposed algorithm's robustness against common attacks, including noise addition, compression, and filtering. The results showcase high-quality image reconstruction, negligible information loss, affirming the scheme's effectiveness in achieving secure image encryption.
This paper proposes a new feature representation methodology for graph-based data. Initially, random walks on matrices of pairwise data similarities are considered. A diffusion process is embedded into orthonormal dec...
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This paper proposes a new feature representation methodology for graph-based data. Initially, random walks on matrices of pairwise data similarities are considered. A diffusion process is embedded into orthonormal decompositions of such matrices at various scales while enabling a data reduction mechanism as well. At each scale, the qr orthonormal decomposition algorithm, alternating with diffusions and data reduction stages is applied recursively on the given graph-based data representations. The proposed methodology is used in extracting complex feature representations from images, which are then used for image matching and in face recognition. In the face recognition application, both global appearance models and semantic representations of biometric features are considered. Both the correlation and the covariance of images of human faces are considered for the training stage when using global appearance models. The proposed data representation is shown to be robust in face recognition applications, when face images are represented in low resolution and when they are corrupted by noise. (C) 2015 Elsevier Ltd. All rights reserved.
Let T-Lambda be the compact manifold of real symmetric tridiagonal matrices conjugate to a given diagonal matrix Lambda with simple spectrum. We introduce bidiagonal coordinates, charts defined on open dense domains f...
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Let T-Lambda be the compact manifold of real symmetric tridiagonal matrices conjugate to a given diagonal matrix Lambda with simple spectrum. We introduce bidiagonal coordinates, charts defined on open dense domains forming an explicit atlas for T-Lambda. In contrast to the standard inverse variables, consisting of eigenvalues and norming constants, every matrix in T-Lambda now lies in the interior of some chart domain. We provide examples of the convenience of these new coordinates for the study of asymptotics of isospectral dynamics, both for continuous and discrete time. (C) 2008 Elsevier Inc. All rights reserved.
For the direction of arrival (DOA) in array signal processing, eigenvalue decomposition (EVD) is one key issue in hardware implementation of the multiple signal classification (MUSIC) algorithm. Therefore, we introduc...
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For the direction of arrival (DOA) in array signal processing, eigenvalue decomposition (EVD) is one key issue in hardware implementation of the multiple signal classification (MUSIC) algorithm. Therefore, we introduce the look-ahead simplified one-sided Jacobi's method to efficiently decompose those symmetric matrices in this article and prove that the new method has the best orthogonality of eigenvector and locates eigenvectors closest to the true solution in theory. Both the numerical performance and real-time are important in engineering, so we present the novel flexible hardware architecture in single floating point arithmetic for EVD on field-programmable gate arrays (FPGAs). Finally, the simulated and raw data are used to investigate the performance of some different approaches in the context of both the EVD and MUSIC algorithm. The experimental results show that our proposed method has the best performance.
The BR algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. It is a bulge-chasing algorithm like the qr algorithm, but, unlike the qr algorithm, it is well adapted to c...
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The BR algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. It is a bulge-chasing algorithm like the qr algorithm, but, unlike the qr algorithm, it is well adapted to computing the eigenvalues of the narrow-band, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes the BR algorithm and gives numerical evidence that it works well in conjunction with the Lanczos process. On the biggest problems run so far, the BR algorithm beats the qr algorithm by a factor of 30-60 in computing time and a factor of over 100 in matrix storage space.
For many years techniques from numerical analysis have been applied fruitfully to the study of dynamical systems. In this paper it is shown that the theory of dynamical systems may be applied to certain computational ...
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For many years techniques from numerical analysis have been applied fruitfully to the study of dynamical systems. In this paper it is shown that the theory of dynamical systems may be applied to certain computational problems. In particular the question of global convergence of various qr algorithms can be reduced to the study of certain vector iterations derived from Schur forms of matrices. The technique is illustrated in determining the convergence behavior of normal Hessenberg matrices under the Francis and multishift qr iterations.
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