Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive high-dimensional problems. Iterative random sparsification allow the estimation of a single dominant eigenvalue at reduced cost by leveraging repeated sampling and averaging. We present general approach to extending such multiple demonstrate its performance several benchmark problems in quantum chemistry.

Genetic algorithms are typically implemented as a computer simulation in which a population of abstract representations (called chromosomes) of candidate solutions (called individuals) to an optimization problem evolves toward better solutions. Traditionally, solutions are represented in binary as strings of 0s and 1s, but different encodings are also possible. The evolution starts from a popul...

We propose a new method of the Single Transferable Vote (STV) and give a unified way to describe classic procedures (Gregory Method, Inclusive Gregory Method and Weighted Inclusive Gregory Method) as an iterative procedure. A modification for quota definition is proposed which improves theoretical properties of the procedures. The method is justified by a new set of axioms. It is shown that thi...

We propose a new method for conducting Single Transferable Vote (STV) elections and provide a unified method for describing classic STV procedures (the Gregory Method, the Inclusive Gregory Method and the Weighted Inclusive Gregory Method) as an iterative procedure. We also propose a modification for quota definition that improves the theoretical properties of the procedures. The method is just...

In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and gradient estimates are inexact possibly random. The assumed to be bounded in absolute without any additional assumptions. We extend the framework based on stochastic methods from [C. Cartis K. Scheinberg, Math. Program., 169 (2018), pp. 337--375] which w...

In this paper, we introduce a modified variational iteration method for second order initial value problems by transforming the integral of iteration process. The main advantages of this modification are that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of conventional variational iteration method. The method is appli...

In this paper, a Van der Pol oscillator containing a periodic oscillator is considered. A simple and effective iteration procedure to search the solution of the modified Van der Pol oscillator equation is proposed. This procedure is a powerful tool for determination of periodic solution of a non-linear equation of motion. The solutions obtained using the present iteration procedure are in good ...

Analyzing the nonlinear vibration of beams is one of the important issues in structural engineering. According to this, an impressive analytical method which is called Modified Iteration Perturbation Method (MIPM) is used to obtain the behavior and frequency of a cantilever beam with geometric nonlinear. This new method is combined by the Mickens and Iteration methods. Moreover, this method don...

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