In this paper, an approximate formula of the fractional derivatives (Caputo sense) is derived. The proposed formula is based on the generalized Laguerre polynomials. Special attention is given to study the convergence analysis of the presented formula. The spectral Laguerre collocation method is presented for solving a class of fractional optimal control problems (FOCPs). The properties of Lagu...

Gradient iterations for the Rayleigh quotient are simple and robust solvers to determine a few of the smallest eigenvalues together with the associated eigenvectors of (generalized) matrix eigenvalue problems for symmetric matrices. Sharp convergence estimates for the Ritz values and Ritz vectors are derived for various steepest descent/ascent gradient iterations. The analysis shows that poores...

In this paper, the authors consider problem of synthesis dual program control for a multidimensional dynamic system and propose various quality indexes control. Based on Rayleigh–Ritz method, they synthesize law spatial position sensor unit in an inertial navigation system.

We present a new numerical iterative method for computing selected eigenpairs of a right definite two-parameter eigenvalue problem. The method works even without good initial approximations and is able to tackle large problems that are too expensive for existing methods. The new method is similar to the Jacobi–Davidson method for the eigenvalue problem. In each step, we first compute Ritz pairs...

Abstract A variational principle is established by the semi-inverse method and used to solve approximately a nonlinear problem Ritz method. In this process,it may be difficult large system of algebraic equations,the Groebner bases theory (Buchberger’s algorithm) applied problem. The results show that approach much simpler more efficient.

The aim of this paper is to provide a convergence analysis for a preconditioned subspace iteration, which is designated to determine a modest number of the smallest eigenvalues and its corresponding invariant subspace of eigenvectors of a large, symmetric positive definite matrix. The algorithm is built upon a subspace implementation of preconditioned inverse iteration, i.e., the well-known inv...