New simultaneous root-finding methods with accelerated convergence for analytic functions

A family of root-finding methods with accelerated convergence

Keywords--Determinat ion of polynomial zeros, Simultaneous iterative methods, Convergence analysis, Accelerated convergence, R-order of convergence. 1. I N T R O D U C T I O N The problem of determining polynomial zeros has a great impor tance in theory and practice (for instance, in the theory of control systems, digital signal processing, s tabil i ty of systems, analysis of transfer function...

A new family of four-step fifteenth-order root-finding methods with high efficiency index

‎In this paper a new family of fifteenth-order methods with high efficiency index is presented‎. This family include four evaluations of the function and one evaluation of its first derivative per iteration.‎ ‎Therefore‎, ‎this family of methods has the efficiency index which equals 1.71877‎. ‎In order to show the applicability and validity of the class‎, ‎some numerical examples are discussed‎.

Accelerated Root Finding for Computational Finance

A parallel implementation of root finding on an SIMD application accelerator is reported. These are roots of stochastic differential equations in the computational finance domain which require a stochastic simulation to be performed for each evaluation of the pricing function. Experiments show that a speedup of 15X can be achieved over using a stand-alone CPU processor, depending on the require...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

New iterative methods with seventh-order convergence for solving nonlinear equations

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.