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In this paper, we provide a structure-preserving one-sided cyclic Jacobi method for computing the singular value decomposition of a quaternion matrix. In this method, the columns of the quaternion matrix are orthogonalized in pairs by using a sequence of orthogonal JRSsymplectic Jacobi matrices to its real counterpart. The quadratic convergence is also established under some mild conditions. Numerical tests are reported to illustrate the efficiency of the proposed method.

In this article, we consider the stochastic inverse singular value problem (ISVP) of constructing a stochastic matrix from the prescribed realizable singular values. We propose a Riemannian inexact Newton-CG method with various choices of forcing terms for solving the stochastic ISVP. We show the proposed method converges linearly or superlinearly for different forcing terms under some assumptions. We also extend the proposed method to the case of prescribed entries. Finally, we report some numerical results to demonstrate the effectiveness of the proposed method.

This investigation discusses the problems of fixed-/predefined-time stabilization and synchronization of memristor chaotic circuits (MCCs). Specially, all of the proposed control schemes are differentiable, namely smooth, which are superior to the previous finite-/fixed-time control techniques, because the discontinuous signum and absolute functions are not contained anymore. Comparing with the traditional fast convergence of chaotic systems, the upper-bound estimation of convergence time in this investigation is not only irrelevant to the initial values of MCCs, but also concise and explicit. Moreover, according to the Lyapunov stability theory, the sufficient criteria are established successively for ensuring the fixed-/predefined-time stabilization and synchronization of MCCs. Finally, the numerical simulations are placed to validate the effectiveness and feasibility of obtained results, in which the comparison is made and the effect of controlling parameters on the convergence speed is further explored.