Approximate Newton methods are standard optimization tools which aim to maintain the benefits of Newton’s method, such as a fast rate of convergence, while alleviating its drawbacks, such as computationally expensive calculation or estimation of the inverse Hessian. In this work we investigate approximate Newton methods for policy optimization in Markov decision processes (MDPs). We first analy...

In this paper we consider generalized Gevrey classes defined in terms of Newton polyhedra. In such functional frame we prove a theorem of solvability of the Cauchy Problem for a class of partial differential operators, called multi-quasi-hyperbolic. We then give a result of regularity of the solution with respect to the space variables and finally analyze the regularity with respect to the time...

For a one-parameter deformation of an analytic complex function germ of several variables, there is defined its monodromy zeta-function. We give a Varchenko type formula for this zeta-function if the deformation is non-degenerate with respect to its Newton diagram.

We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in wide class of modified theories gravity. The utilizes relaxed Newton-Raphson method solve the full nonlinear Einstein's equations on two-dimensional grid with Newton polynomial finite difference scheme. validate this by considering static and holes general r...

The Newton radius of a code is the largest weight of a uniquely correctable error. The covering radius is the largest distance between a vector and the code. Two relations between the Newton radius and the covering radius are given.

We consider a Newton-Krylov approach for discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is essential for obtaining an efficient solver in such an approach. In this paper we compare point-block-Gauss-Seidel, point-block-ILU and point-block-SPAI preconditioners. It turns out that the SPAI method is not satisfactory for our problem class. The point-bl...

Abstract. In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as GaussNewton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then update the iteration point by a Gauss-Newton iteration step. We prove that a re-sampled version of this algorithm quadratically converges to the solution...

Resistant training in radial basis function (RBF) networks is the topic of this paper. In this paper, one modification of Gauss-Newton training algorithm based on the theory of robust regression for dealing with outliers in the framework of function approximation, system identification and control is proposed. This modification combines the numerical robustness of a particular class of non-quad...

In this paper, a recursive Gauss-Newton (RGN) algorithm is first developed for adaptive tracking of the amplitude, frequency and phase of a real sinusoid signal in additive white noise. The derived algorithm is then simplified for computational complexity reduction as well as improved with the use of multiple forgetting factor (MFF) technique to provide a flexible way of keeping track of the pa...