FAST ARRAY ALGORITHMS FOR FILTERING OF MARKOVIAN JUMP LINEAR SYSTEMS WITH STRUCTURED TIME-VARIANT PARAMETERS

In this paper were developed fast array algorithms for the linear minimum mean square error estimator for a class of Markovian jump linear systems with structured time-variant parameters. The fast array algorithms for systems with structured time-variant parameters arises as an alternative to calculate this type algorithm for some variation in the time of the parameters. Numerical example to show the advantage of using fast array algorithm to filter this class of systems are provided.

On the derivative-free quasi-Newton-type algorithm for separable systems of nonlinear equations

A derivative-free quasi-Newton-type algorithm in which its search direction is a product of a positive definite diagonal matrix and a residual vector is presented. The algorithm is simple to implement and has the ability to solve large-scale nonlinear systems of equations with separable functions. The diagonal matrix is simply obtained in a quasi-Newton manner at each iteration. Under some suitable conditions, the global and R-linear convergence result of the algorithm are presented. Numerical test on some benchmark separable nonlinear equations problems reveal the robustness and efficiency of the algorithm.