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In this paper we propose a structure-preserving doubling algorithm (SDA) for computing the minimal nonnegative solutions to the nonsymmetric algebraic Riccati equation (NARE) based on the techniques developed in the symmetric cases. This method allows the simultaneous approximation of the minimal nonnegative solutions of the NARE and its dual equation, only(More)
We study canonical forms for Hamiltonian and symplectic matrices or pencils under equivalence transformations which keep the class invariant. In contrast to other canonical forms our forms are as close as possible to a triangular structure in the same class. We give necessary and suucient conditions for the existence of Hamiltonian and symplectic triangular(More)
The inverse eigenvalue problem of constructing real and symmetric square matrices M, C and K of size n × n for the quadratic pencil Q(λ) = λ 2 M + λC + K so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors is considered. This paper consists of two parts addressing two related but different problems. The first part deals with the inverse(More)
From the necessary and sufficient conditions for complete reachability and observability of periodic time-varying descriptor systems, the symmetric positive semi-definite reachabil-ity/observability Gramians are defined. These Gramians can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method(More)
In this paper, we propose a digitalized chaotic map, Variational Logistic Map (VLM), modified from classical logistic map to be used in secure communication. Compared with classical logistic map, VLM has large parameter space without windows and can be implemented at low hardware cost. Referring to statistical testing suites SP800-22 and TestU01, VLM with(More)
The following nonlinear latent value problem is studied: F(h)x = 0, where F(h) is an n X n analytic nondefective matrix function in the scalar A. The latent pair (A, x) has been previously found by applying Newton's method to a certain equation. The deflation technique is required for finding another latent pair starting from a computed latent pair. Several(More)
In this paper, we consider the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C, and K of size n × n, with (M, C, K) / = 0, so that the quadratic matrix polynomial Q(λ) = λ 2 M + λC + K has m (n < m 2n) prescribed eigenpairs. It is shown that, for almost all prescribed eigenpairs, the QIEP has a solution with M(More)
We consider the quadratic eigenvalues problem (QEP) of gyroscopic systems (λ 2 M + λG + K)x = 0, with M = M being positive definite, G = −G , and K = K being negative semidefinite. In [1], it is shown that all eigenvalues of the QEP can be found by finding the maximal solution of a nonlinear matrix equation Z + A Z −1 A = Q under the assumption that the QEP(More)
We consider the solution of the-AXA ± BY B = C and AXB ± (AXB) = C). Solvability conditions and stable numerical methods are considered, in terms of the (generalized and periodic) Schur, QR and (generalized) singular value decompositions. We emphasize on the square cases where m = n but the rectangular cases will be considered. The-sylvester equation is(More)