A deeation procedure is introduced that is designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix. As the iteration progresses the Ritz value approximations of the eigenvalues of A converge at diierent rates. A numerically stable scheme is introduced that implicitly deeates the converged approximations from the iteratio...

We extend the Adomian's decomposition method to work for the general eigenvalue problems, in addition to the existing applications of the method to boundary and initial value problems with nonlinearity. We develop the Hamiltonian inverse iteration method which will provide the ground state eigenvalue and the explicit form eigenfunction within a few iterations. The method for finding the excited...

we introduce and discuss the homotopy perturbation method, the adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. then, we give an example of the stefan problem with  kinetics and solve it by these methods.

We analyze controllability properties of the inverse iteration and the QR-algorithm equipped with a shifting parameter as a control input. In the case of the inverse iteration with real shifts the theory of universally regular controls may be used to obtain necessary and suucient conditions for complete controllability in terms of the solvability of a matrix equation. Partial results on conditi...

in this paper, we have proposed a new iterative method for finding the solution of ordinary differential equations of the first order. in this method we have extended the idea of variational iteration method by changing the general lagrange multiplier which is defined in the context of the variational iteration method.this causes the convergent rate of the method increased compared with the var...

In this paper, we have proposed a new iterative method for finding the solution of ordinary differential equations of the first order. In this method we have extended the idea of variational iteration method by changing the general Lagrange multiplier which is defined in the context of the variational iteration method.This causes the convergent rate of the method increased compared with the var...

In this paper, we discuss vector and parallel tuning of GeoFEM and the Householder QR decomposition process being solid earth simulation codes. Process of GeoFEM code can be roughly divided into two parts, Matrix Assemble part and Solver part. Currently, GeoFEM's parallel iterative solver has attained good parallel and vector performance, and GeoFEM's Matrix Assemble part has attained good para...

In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a preconditioner for solving symmetric positive definite linear systems of equations by using the preconditioned conjugate gradient algorithm. Some numerical experime...

We adapt the inverse iteration method for symmetric matrices to some nonlinear PDE eigenvalue problems. In particular, for p ∈ (1,∞) and a given domain Ω ⊂ Rn, we analyze a scheme that allows us to approximate the smallest value the ratio ∫ Ω |Dψ| pdx/ ∫ Ω |ψ| pdx can assume for functions ψ that vanish on ∂Ω. The scheme in question also provides a natural way to approximate minimizing ψ. Our an...