Results 271 to 280 of about 3,545,396 (319)

Matrix Symmetrization

Journal of Guidance, Control, and Dynamics, 1998
Summary: In this note we point out that the symmetrized real matrix is also the symmetric matrix that is the closest, in the Euclidean norm, to the matrix being symmetrized. This implies that, when symmetrizing the solutions to Riccati and Lyapunov equations, one actually replaces the solution by its closest symmetric matrix.
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Determinant of the Sum of a Symmetric and a Skew-Symmetric Matrix

SIAM Journal on Matrix Analysis and Applications, 1997
Assume \(\alpha=(\alpha_1\geq\ldots\geq\alpha_n)\), and \(\beta=(\beta_1=\beta_2\geq\beta_3=\beta_4\geq\ldots\geq\beta_n)\), where \(\beta_n=0\) if \(n\) is odd. Using standard notation, write \(\widetilde A=\text{diag}(\alpha_n,\ldots,\alpha_1)\), \(\widetilde B=\sum_{k\leq n/2}\beta_{2k}(E_{2k-1,2k}-E_{2k,2k-1})\).
Bebiano, Natália, Li, Chi-Kwong, da Providência, João   +2 more
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An algorithm for matrix symmetrization

Journal of the Franklin Institute, 1981
Abstract In this paper we characterize a symmetrizability property using the theory of output sets. Employing the basic properties of symmetric matrices and an efficient algorithm for systematic generation of output sets, an algorithm for testing the symmetrizability of a matrix is presented and illustrated.
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Multi-document summarization via sentence-level semantic analysis and symmetric matrix factorization

Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, 2008
Multi-document summarization aims to create a compressed summary while retaining the main characteristics of the original set of documents. Many approaches use statistics and machine learning techniques to extract sentences from documents. In this paper,
Dingding Wang, Tao Li, Shenghuo Zhu, C. Ding   +3 more
semanticscholar   +1 more source

Mass matrix with symmetric mixing

Physical Review D, 1991
Extending the work of Barnhill, we propose distributing the mixing matrix between the up and down quarks equally. With this choice of gauge eigenstates, the resulting mixing matrix in the new basis is simply the identity and the gauge bosons couple to these states in an essentially trivial manner.
T. S. Santhanam, V. V. Dixit, W. D. Thacker   +2 more
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Symmetric Matrix Means

Linear Algebra and its Applications, 2022
Mitsuru Uchyama
semanticscholar   +1 more source

Symmetric Matrix Eigenvalue Techniques

2006
The article describes symmetric matrix eigenvalue techniques: basic methods (power method, inverse iteration, orthogonal iteration and QR iteration), tridiagonalization and implicitly shifted QR method, divide-and-conquer method, bisection and inverse iteration, the method of multiple relatively robust representations, Jacobi method and Lanczos method.
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Minimizing the Profile of a Symmetric Matrix

SIAM Journal on Scientific Computing, 2002
Two classes of methods for optimizing the profile of a sparse matrix are given. Profile storage is useful when the matrix is moderately sparse, or when the nonzero entries are near the main diagonal. The proposed methods in the first class are heuristic.
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The gradient with respect to a symmetric matrix

IEEE Transactions on Automatic Control, 1977
The well-known formulas for gradient matrices can be applied only when the elements of the matrix are independent [1],[2]. In this note, the author derives gradient formulas for two important types of element dependency: symmetry and skew symmetry. Application is made to the sensitivity analysis of optimal estimation systems.
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Computation of an eigenvector of a symmetric tridiagonal matrix

Siberian Mathematical Journal, 1986
A new algorithm for the computation of an eigenvector of a symmetric tridiagonal matrix is given with error estimation. This estimation depends only on the order of numbers in the computer.
V. I. Kostin, A. D. Mitchenko, S. K. Godunov   +2 more
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