This paper computes the optimal control and state of the one-dimensional Energized wave equation using the Extended Conjugate gradient Method (ECGM. We recalled all vital computational issues in the implementation of the ECGM algorithm on the one-dimensional Energized Wave equation in the paper. With these recalls, program codes were derived which gave various numerical optima controls and stat...

The paper computes the optimal control and state of the two-dimensional Energized wave equation using the Extended Conjugate gradient Method (ECGM). This piece of work has to do with all the vital computational elements as derived in the implementation of the ECGM algorithm on the two-dimensional Energized Wave equation in (Waziri, 1) and (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [7-9]). Wit...

Based on an eigenvalue analysis, a new proof for the sufficient descent property of the modified Polak-Ribière-Polyak conjugate gradient method proposed by Yu et al. is presented.

In this article we report on our efforts to test and expand the current state-of-the-art in eigenvalue solvers applied to the field of nanotechnology. We singled out the nonlinear conjugate gradients (CG) methods as the backbone of our efforts for their previous success in predicting the electronic properties of large nanostructures and made a library of three different solvers (two recent and ...

In this paper, we considered the role of penalty when the higher-order conjugate gradient method (HCGM) was used as a computational scheme for the minimization of penalised cost functions for optimal control problems described by linear systems and integral quadratic costs. For this family of commonly encountered problems, we find out that the conventional penalty methods require very large pen...

The paper proposes a preconditioner for the conjugate gradient method CG that is designed for solving systems of equations Ax bi with di erent right hand side vec tors or for solving a sequence of slowly varying systems Akx bk The preconditioner has the form of a limited memory quasi Newton matrix and is generated using infor mation from the CG iteration The automatic preconditioner does not re...

Aggregation-based multigrid with standard piecewise constant like prolongation is investigated. Unknowns are aggregated either by pairs or by quadruplets; in the latter case the grouping may be either linewise or boxwise. A Fourier analysis is developed for a model twodimensional anisotropic problem. Most of the results are stated for an arbitrary smoother (which fits with the Fourier analysis ...

We study numerical methods for the solution of general linear moment problems, where the solution belongs to a family of nested subspaces of a Hilbert space. Multi-level algorithms, based on the conjugate gradient method and the Landweber–Richardson method are proposed that determine the “optimal” reconstruction level a posteriori from quantities that arise during the numerical calculations. As...

Recently, the authors obtained an upper bound on the error for the conjugate gradient method, which is valid in an asymptotic setting as the size of the linear systems tends to innnity. The estimate depends on the asymptotic distribution of eigenvalues, and the ratio between the size and the number of iterations. Such error bounds are related to the existence of polynomials with value 1 at 0 wh...

The composite step biconjugate gradient method (CSBCG) is a simple modification of the standard biconjugate gradient algorithm (BCG) which smooths the sometimes erratic convergence of BCG by computing only a subset of the iterates. We show that 2 × 2 composite steps can cure breakdowns in the biconjugate gradient method caused by (near) singularity of principal submatrices of the tridiagonal ma...