In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate,...

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

in this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable taylor and weight function approximation. the method is based on weerakoon-fernando method [s. weerakoon, g.i. fernando, a variant of newton's method with third-order convergence, appl. math. lett. 17 (2000) 87-93]. the method is optimal, as it needs three evaluations per ite...

We present and implement a fourth-order projective dependency parsing algorithm that effectively utilizes both “grand-sibling” style and “tri-sibling” style interactions of third-order and “grand-tri-sibling” style interactions of forth-order factored parts for performance enhancement. This algorithm requires O(n5) time and O(n4) space. We implement and evaluate the parser on two languages—Engl...