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...

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...

This paper presents an iterative algorithm for solving intuitionistic fuzzy nonlinear equations (IFNEs). The proposed method is based on the classical conjugate gradient (CG) search direction. An interesting feature of new that it considers problems special triangular number. For this purpose, quantities are transformed into membership and non-membership parametric forms, a line procedure emplo...

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 mixed hybrid nite element discretization of Darcy's law and continuity equation describing the potential uid ow problem in porous media leads to a symmetric indeenite linear system for the pressure and velocity vector components. As a method of solution the reduction to Schur complement systems based on successive block elimination is considered. The computational complexity of a direct sol...

In Hybrid Monte Carlo simulations for full QCD, the gauge fields evolve smoothly as a function of Molecular Dynamics time. Here we investigate improved methods of estimating the trial or starting solutions for the Dirac matrix inversion as superpositions of a chronological sequence of solutions in the recent past. By taking as the trial solution the vector which minimizes the residual in the li...

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 ...

In this paper, the Dai-Kou type conjugate gradient methods are developed to solve the optimality condition of an unconstrained optimization, they only utilize gradient information and have broader application scope. Under suitable conditions, the developed methods are globally convergent. Numerical tests and comparisons with the PRP+ conjugate gradient method only using gradient show that the m...