A parallel root-finding algorithm

Abstract

We present a parallel algorithm to calculate a numerical approximation of a single, isolated root α of a function f : R → R which is sufficiently regular at and around α. The algorithm is derivative free and performs one function evaluation on each processor per iteration. It requires at least three processors and can be scaled up to any number of these. The order with which the generated sequence of approximants converges to α is equal to (n + √ n 2 + 4)/2 for n + 1 processors with n 2. This assumes that particular combinations of the derivatives of f do not vanish at α.

An Optimized Newton-Raphson Algorithm for Approximating Internal Rate of Return

“…It is a challenging task in scientific application problems to estimate the solution of non-linear equations [2], the function of IRR being one of them [17], as well as trial calculation, which may take numerous hours [18]. A more efficient way to estimate is by using a root-finding algorithm an iterative calculation scheme to approximate a single, isolated root of a function f(IRR), where the root IRR is a solution of the equation f(IRR) = 0 [12]. IRR is the most widely-used method in measuring the feasibility of a project or investment [4]- [6].…”

“…It is one of the tools that helps an intelligent enterprise in their decision making processes, which may help them in realizing certain goals [9]. However, IRR cannot be isolated in the equation and cannot be determined analytically, which led researchers to use iterative algorithms in estimating IRR [12], [17].…”