Search results for "Symmetric matrix"
showing 4 items of 14 documents
Diagonalization of large matrices: a new parallel algorithm.
2015
On the basis of a dressed matrices formalism, a new algorithm has been devised for obtaining the lowest eigenvalue and the corresponding eigenvector of large real symmetric matrices. Given an N × N matrix, the proposed algorithm consists in the diagonalization of (N - 1)2 × 2 dressed matrices. Both sequential and parallel versions of the proposed algorithm have been implemented. Tests have been performed on a Hilbert matrix, and the results show that this algorithm is up 340 times faster than the corresponding LAPACK routine for N = 10(4) and about 10% faster than the Davidson method. The parallel MPI version has been tested using up to 512 nodes. The speed-up for a N = 10(6) matrix is fair…
Improvement of matrix solutions of generalized nonlinear wave equation
2005
Four classes of nonlinear wave equations are joined in one generalized nonlinear wave equation. A theorem is proved that the whole series of matrix functions satisfy the generalized wave equation. A justification of rotational properties of matrix solutions is given and a mathematical model of the ring vortex around the acute edge is proposed using of matrix solutions.
H<inf>&#x221E;</inf> filter design for time-delay Markovian jump systems
2013
This paper investigates the H ∞ filtering problem for discrete time-delay Markovian jump systems with application to networked control systems. To design a full-order filter which ensures the stochastic stability and a prescribed H ∞ performance level for the filtering error system, the Scaled Small Gain (SSG) Theorem is developed for stochastic systems. By employing a two-term approximation to delayed state variables, the original system is transformed into an input-output form consisting of two subsystems. Based on the developed SSG Theorem and the proposed Lyapunov-Krasovskii Functional (LKF), the scaled small gains of the subsystems are analyzed to establish a new condition for the exis…
Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices
2006
In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estima…