To compute the smallest eigenvalues and associated eigenvectors of a real symmetric matrix, we consider the Jacobi–Davidson method with inner preconditioned conjugate gradient iterations for the arising linear systems. We show that the coe9cient matrix of these systems is indeed positive de:nite with the smallest eigenvalue bounded away from zero. We also establish a relation between the residu...

The conjugate gradient methods are outstanding by choosing a suitable for coefficient conjugate. In this paper, modified version of the algorithm suggested Hideaki and Yasushi [4] is proposed in order to show that new method globally convergent, under standard assumptions. To exemplify efficiency method, its performance examined impulse noise removal images.

In this paper, the Newton-conjugate-gradient methods are developed for solitary wave computations. These methods are based on Newton iterations, coupled with conjugategradient iterations to solve the resulting linear Newton-correction equation. When the linearization operator is self-adjoint, the preconditioned conjugate-gradient method is proposed to solve this linear equation. If the lineariz...

It is shown that the four vector extrapolation methods, minimal polynomial extrapolation, reduced rank extrapolation, modified minimal polynomial extrapolation, and topological epsilon algorithm, when applied to linearly generated vector sequences, are Krylov subspace methods, and are equivalent to some well known conjugate gradient type methods. A unified recursive method that includes the con...

T study was motivated primarily by the author’s interest in numerical methods at both a teaching and research level. Much has already been written about “standard” Mathcad 6 and the purpose of this article is to focus on, and use, some of the features of Plus 6 which are not available in the standard version. In particular the use of the programming facility, which comes with Plus 6, is illustr...

Sensitivity analysis on Sea Surface Temperature: SST estimation with Thermal Infrared Radiometer: TIR data through simulations is conducted. Also Conjugate Gradient Method: CGM based SST estimation method is proposed. SST estimation error of the proposed CGM based method is compared to the conventional Split Window Method: SWM with a variety of conditions including atmospheric models. The resul...

Abstract: The conjugate gradient method is an algorithm for the numerical solution of systems of linear equations whose matrices are positive-definite and symmetric. It is an iterative method that can even be applied to solve a sparse system of equations. In this paper, we applied the conjugate gradient method of higher order to wave propagation control problems. The algorithm of this method wa...

In this paper, a new conjugate conjugate method with sufficient descent property is proposed for the unconstrained optimization problem. An attractive property of the new method is that the descent direction generated by the method always possess the sufficient descent property, and this property is independent of the line search used and the choice of ki  . Under mild conditions, the global c...

In this paper, we propose a new nonlinear conjugate gradient method for large-scale unconstrain optimization which possesses the following properties:(i)the sufficient descent condition −g k dk ≥ 7 8 ‖gk‖ 2 holds without any line searches;(ii)With exact line search, this method reduces to a nonlinear version of the Liu-Storey conjugate gradient scheme.(iii)Under some assumption, global converge...