We present a new hybrid algorithm based on Godunov’s method for computing eigenvectors of symmetric tridiagonal matrices and Inverse Iteration, which we call the Godunov–Inverse Iteration. We use eigenvectors computed according to Godunov’s method as starting vectors in the Inverse Iteration, replacing any nonnumeric elements of Godunov’s eigenvectors with random uniform numbers. We use the rig...

The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called the Variational Iteration Method (VIM) and the correspondent approximated solutions will be obtained for the P-M equation with regards to relevant error analysis. Thr...

Let {ak}, k = 1, . . . , N be a family of matrices of sizes rk × rk−1. For positive integers i, j, i > j define the operation aij as follows: a × ij = ai−1 · · ·aj+1 for i > j + 1, aj+1,j = Irj . Let {bk}, k = 1, . . . , N be a family of matrices of sizes rk−1 × rk. For positive integers i, j, j > i define the operation bij as follows: b × ij = bi+1 · · · bj−1 for j > i+ 1, bi,i+1 = Iri . It is...

Variational iteration method is applied to examine the temperature distribution within a single fin with a one-dimensional steady-state nonlinear heat conduction equation. Variation of temperature due to different levels of nonlinearities is analyzed. The results obtained by means of variational iteration method are compared with the results obtained from finite element method. A fourth iterati...

In this paper, the variational iteration method is used to solve the Cauchy problem. Some examples are given to elucidate the solution procedure and reliability of the obtained results. The variational iteration algorithm leads to exact solutions in the present study. © 2010 Elsevier Ltd. All rights reserved.

In this paper, we revisit the D-iteration algorithm in order to better explain different performance results that were observed for the numerical computation of the eigenvector associated to the PageRank score. We revisit here the practical computation cost based on the execution runtime compared to the theoretical number of iterations.

In this paper, we report the application of two parameter coupled alternating group explicit (CAGE) iteration and Newton-CAGE iteration methods for the cubic spline solution of non-linear differential equation u" = f(r,u,u') subject to given natural boundary conditions. The error analysis for CAGE iteration method is discussed in details. We compared the results of proposed CAGE iteration metho...

This paper deals with computational algorithms for obtaining the optimal stationary policy and the minimum cost of a discounted semi-Markov decision process. Van Nunen [23) has proposed a modified policy iteration algorithm with a suboptimality test of MacQueen type, where the modified policy iteration algorithm is policy iteration method with the policy evaluation routine by a finite number of...