We developed a fast numerical method for complex symmetric shifted linear systems, which is motivated by the quantum-mechanical (electronicstructure) theory in nanoscale materials. The method is named shifted Conjugate Orthogonal Conjugate Gradient (shifted COCG) method. The formulation is given and several numerical aspects are discussed.

A novel method of function minimization that combines the power of the diagonal approximation to the normal matrix with conjugate directions is described. This method approaches closer to the local minimum than the methods that are commonly used in macromolecular refinement. The weakness of the current methods are analyzed to explain the advantage of the conjugate-direction method.

The Steepest descent method and the Conjugate gradient to minimize nonlinear functions have been studied in this work. Algorithms are presented implemented Matlab software for both methods. However, a comparison has made between method. obtained results time efficiency aspects. It is shown that needs fewer iterations more than On other hand, converges function less

In view of the small sample size combat ammunition trial data and difficulty forecasting demand for ammunition, a Bayesian inference method based on multinomial distribution is proposed. Firstly, considering different damage grades hitting targets, results are approximated as distribution, model established, which provides theoretical basis multigrade under condition samples. Secondly, conjugat...

Treatment methods for breast cancer are not specific and each one has its own drawbacks. For this reason, scientists are seeking ways in which specifically affect cancer cells. Photothermal therapy is a method that uses near-infrared (NIR) laser energy to create sufficient heat to destroy cancer cells. In this study, the photothermal effect of gold nanorods (GNRs) was investigated for breast ca...

Treatment methods for breast cancer are not specific and each one has its own drawbacks. For this reason, scientists are seeking ways in which specifically affect cancer cells. Photothermal therapy is a method that uses near-infrared (NIR) laser energy to create sufficient heat to destroy cancer cells. In this study, the photothermal effect of gold nanorods (GNRs) was investigated for breast ca...

The smoothing procedure has been introduced by Schh onauer as an acceleration algorithm for the Generalized Conjugate Gradient methods. In this paper, after giving our deenition of Conjugate Gradient type methods, and using a Generalized Hessenberg process, we introduce a Hybrid generalized Conjugate Gradient type method. We show that this Hybrid procedure is a variable smoothing procedure. And...

1 ABSTRACT In this paper we propose a new line search algorithm that ensures global convergence of the Polak-Ribi ere conjugate gradient method for the unconstrained minimization of nonconvex diierentiable functions. In particular, we show that every limit point produced by the Polak-Ribi ere iteration is a stationary point of the objective function. Moreover, we prove that, asymptotically, the...

In the eld of computational electrodynamics the discretization of Maxwell's equations using the Finite Integration Theory (FIT) yields very large, sparse, complex symmetric linear systems of equations. For this class of complex non-Hermitian systems a number of conjugate gradient-type algorithms is considered. The complex version of the biconjugate gradient (BiCG) method by Jacobs can be extend...

Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: 1. The Fletcher-Reeves method, the Hestenes-Stiefel method, and the Dai-Yuan method applied to a strongly convex LC objective function; 2. The Polak-Ribière method and the Conjugate ...