In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...

Stochastic approximation (SA) has long been applied for problems of minimizing loss functions or root finding with noisy input information. As with all stochastic search algorithms, there are adjustable algorithm coefficients that must be specified, and that can have a profound effect on algorithm performance. It is known that choosing these coefficients according to an SA analog of the determi...

The proliferation of inverter-based distributed energy resources (IBDERs) has increased the number control variables and dynamic interactions, leading to new grid challenges. For stability analysis designing appropriate protection controls, it is important that IBDER models are accurate. This paper focuses on accurate estimation parameter calibration DER_A, a recently proposed aggregated model....

The subject of this paper is fast numerical algorithms for factoring univariate polynomials with complex coefficients and for computing partial fraction decompositions (PFDs) of rational functions in C(z). Numerically stable and computationally feasible versions of PFD are specified first for the special case of rational functions with all singularities in the unit disk (the ``bounded case'') a...

With the Phase-Root-Seeking algorithm a new and very fast algorithm for time delay estimation was recently introduced, permitting the estimation of strain images in real-time. In this paper the accuracy of the real-time strain imaging concept is investigated by the most rigorous approach, i.e. a comparison to the theoretical accuracy limit: the Cramer-RaoLower-Bound. Simulations show, that this...