Abstract
Newton's and Laguerre's methods can be used to concurrently refine all separated zeros of a polynomial P( z). This paper analyses the rate convergence of both procedures, and its implication on the attainable number n of correct figures. In two special cases the number m of iterations required to reach an accuracy η = 10 − n is shown to grow as log λ n, where λ = 3 for Newton's and λ = 4 for Laguerre's. In the general case m is shown to grow linearly with n for both procedures. An assessment of the efficiency of the two methods is also given, by evaluating the computational complexity of operations in circular arithmetic, and the efficiency indices of the two iterative schemes.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
