About The Root Finder of The High Order Characteristic Equation In Prony Analysis

프로니 해석시 나타나는 고차 특성 방정식 해법에 대하여

Conventional methods for root finding of the algebraic equations are intrinsically synthetic division methods, i.e., which are the factorization in forms of $f(x)=(x-x_i)Q(x)$. So existing methods have some demerits such as deflation and root-polishing procedures. To overcome these defects a new powerful algorithm, namely circular arithmetic algorithm(CSM), was introduced and has been investigated about its fascinating properties. In this paper, we will propose a simple and effective method of getting the initial guesses for the roots of the equation. With this method the CSM can me all the root of equation with great efficiency.