Answer both questions with a minimum of 80 words per question: Discuss how Atkins method can improve the convergence of a numerical scheme Discuss the pros and cons for Netwon's Method for root...

Question 1: Discuss how Atkins method can improve the convergence of a numerical
scheme.
Answer: Atkin’s method is a exclusive way to calculate the number of points of the curve
which is designed over finite fields from partial data obtained in definition is called Match and
Sort Algorithm by Atkins. It helps in improving the convergence by decreasing the complexity
of the bits. Schoof’s deterministic polynomial time algorithm which allows us to execute this
task in O(log8 q) elementary operations was primarily enhanced by Atkin, and Elkies “to yield a
probabilistic algorithm whose...