We apply a coctel of elementary methods to the problem finding roots an arbitrary polynomial. Specifically, we combine properties iteration z → z2 + c with rudimentary Galois theory in order justify algorithm find complex

Dynamic programming is a class of algorithms used to compute optimal control policies for Markov decision processes. ubiquitous in theory, and also the foundation reinforcement learning. In this paper, we show that value improvement, one main steps dynamic programming, can be naturally seen as composition category optics, intuitively, function limit chain optic compositions. We illustrate with ...

In this paper, we consider the stochastic iterative counterpart of value iteration scheme wherein only noisy and possibly biased approximations Bellman operator are available. We call approximate (AVI) scheme. Neural networks often used as function approximators, in order to counter Bellman’s curse dimensionality. they operator. Because neural typically trained using sample data, errors biases ...

This paper examines the reasons for design iteration and describes models of design iteration. Iteration is the process of repeating tasks within a design project, and is common to all types of engineering design. Iteration is typically necessary for two reasons: an unexpected failure of a design or prototype to meet established criteria; and an expected response to information which was genera...

in this paper, elzaki homotopy perturbation method is employed for solving linear and nonlinear differential equations with a variable coffecient. this method is a combination of elzaki transform and homotopy perturbation method. the aim of using elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as homotopy perturbat...

Newton’s iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton’s iteration can be done efficiently. We show that the convergence of the modifie...