This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. ...

Ritz method is one of the techniques for reduction of the degrees of freedom. Efficiency of Ritz method depends on used vectors. The Ritz method uses load depended vectors in spite of modal method and for this reason it is expected to give better results than modal method. This is the advantage of Ritz method. It is worth mention that the mode shapes are independent of loading. The vectors that...

We are concerned with eigenvalue problems for definite and indefinite symmetric matrix pencils. First, Rayleigh-Ritz methods are formulated and, using Krylov subspaces, a convergence analysis is presented for definite pencils. Second, generalized symmetric Lanczos algorithms are introduced as a special Rayleigh-Ritz method. In particular, an a posteriori convergence criterion is demonstrated by...

New restarted Lanczos bidiagonalization methods for the computation of a few of the largest or smallest singular values of a large matrix are presented. Restarting is carried out by augmentation of Krylov subspaces that arise naturally in the standard Lanczos bidiagonalization method. The augmenting vectors are associated with certain Ritz or harmonic Ritz vectors. Computed examples show the ne...

After reviewing the harmonic Rayleigh–Ritz approach for the standard and generalized eigenvalue problem, we discuss different extraction processes for subspace methods for the polynomial eigenvalue problem. We generalize the harmonic and refined Rayleigh–Ritz approach, which are new approaches to extract promising approximate eigenpairs from a search space. We give theoretical as well as numeri...

Interpolation theory is a necessary and crucial tools for many applied engineering sciences. In this paper, we propose a new kind of 2-period interpolation of functions with period 2 at the nodes x k = x k;n = k=n; (k = 0; 1; ; 2n ? 1). We nd out the necessary and suucient conditions for regularity of this new interpolation problem. Moreover, a closed form expression for the interpolation polyn...