In this preliminary work, left and right conjugate vectors are deened for nonsymmetric, nonsin-gular matrices A and some properties of these vectors are studied. A left conjugate direction (LCD) method for solving nonsymmetric systems of linear equations is proposed. The method reduces to the usual conjugate gradient method when A is symmetric positive deenite. A nite termination property of th...

We consider symmetric positive definite systems of linear equations with multiple right-hand sides. The seed conjugate gradient method solves one right-hand side with the conjugate gradient method and simultaneously projects over the Krylov subspace thus developed for the other right-hand sides. Then the next system is solved and used to seed the remaining ones. Rounding error in the conjugate ...

In this study it has been tried, to compare results and convergence rate of sensitivity analysis and conjugate gradient algorithms to reduce fuel consumption and increasing engine performance by optimizing the timing of opening and closing valves in XU7/L3 engine. In this study, considering the strength and accuracy of simulation GT-POWER software in researches on the internal combustion engine...

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...

Conjugate gradient methods are widely used for unconstrained optimization, especially large scale problems. Most of conjugate gradient methods don’t always generate a descent search direction, so the descent condition is usually assumed in the analyses and implementations. Dai and Yuan (1999) proposed the conjugate gradient method which generates a descent direction at every iteration. Yabe and...

We discuss the construction of algebraic multilevel preconditioners for the conjugate gradient method and derive explicit and sharp bounds for the convergence rates. We present several numerical examples that demonstrate the efficiency of the preconditioner. sparse approximate inverse, sparse matrix, algebraic multilevel method, preconditioning, conjugate gradient method, Krylov subspace method...

In this paper, by using the smoothing Fischer-Burmeister function, we present a new smoothing conjugate gradient method for solving the nonlinear nonsmooth complementarity problems. The line search which we used guarantees the descent of the method. Under suitable conditions, the new smoothing conjugate gradient method is proved globally convergent. Finally, preliminary numerical experiments sh...

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...

The conjugate gradient optimization algorithm is combined with the modified back propagation algorithm to yield a computationally efficient algorithm for training multilayer perceptron (MLP) networks (CGFR/AG). The computational efficiency is enhanced by adaptively modifying initial search direction as described in the following steps: (1) Modification on standard back propagation algorithm by ...