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A smooth curve interpolation scheme for positive data is developed. Conditions have been incorporated into this scheme to preserve the shape of the data lying above a line. This scheme uses rational cubic Ball representation. Conditions are derived for preserving positivity and C¹ continuity. The outputs from a number of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

In this paper we present a new search direction known as the CG-BFGS method, which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-BFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent. [ABSTRACT FROM AUTHOR]

Conjugate gradient (CG) methods play a significant and important role in solving unconstrained optimization. This paper presents, a new modification of the conjugate gradient coefficient (βκ) that has global convergence properties. The global convergence result is established using exact line searches. Numerical results show that the proposed formula is superior when compared to other CG coefficients. Numerical results also suggest that this method possesses global convergence properties. [ABSTRACT FROM AUTHOR]