We design a block Krylov method to compute the action of the Fréchet derivative of a matrix function on a vector using only matrix-vector products, i.e., the derivative of f(A)b when A is subject to a perturbation in the direction E. The algorithm we derive is especially effective when the direction matrix E in the derivative is of low rank, while there are no such restrictions on A. Our result...

In this paper, linear matrix inequality (LMI) approach for synchronization of chaotic fuzzy cellular neural networks (FCNNs) with discrete and unbounded distributed delays based on sampled-data controlis investigated. Lyapunov-Krasovskii functional combining with the input delay approach as well as the free-weighting matrix approach are employed to derive several sufficient criteria in terms of...

The theory of finite-rank perturbations allows for the determination spectral information broad classes operators using tools analytic function theory. In this work, are applied to powers derivative operator, providing a full account from self-adjoint boundary conditions computing aspects operators' matrix-valued measures. particular, support and weights Clark (spectral) measures computed via c...

The most popular method for computing the matrix logarithm is the inverse scaling and squaring method, which is the basis of the recent algorithm of [A. H. Al-Mohy and N. J. Higham, Improved inverse scaling and squaring algorithms for the matrix logarithm, SIAM J. Sci. Comput., 34 (2012), pp. C152–C169]. We show that by differentiating the latter algorithm a backward stable algorithm for comput...

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...