Numerical Analysis A 2022 1. Consider the equation e* = COS I (a) Show that there is a solution p € (-1,-1] (b) Consider

[answerhappygod]

Numerical Analysis A 2022 1 Consider The Equation E Cos I A Show That There Is A Solution P 1 1 B Consider 1 (89.44 KiB) Viewed 26 times

Numerical Analysis A 2022 1. Consider the equation e* = COS I (a) Show that there is a solution p € (-1,-1] (b) Consider the following iterative methods (i) xk+1 = ln (cos Ik) and (ii) Ik+1 = arccos (ek) Are these methods guaranteed to convergence to p? Show your working. 2. A root p of f(x) is said to have multiplicity m if Paper A f(x) = (x − p)q(x) [2] [8] where limx→p g(x) + 0. Show that the Newton's method converges linearly to roots of multiplicity m > 1. [7] . (a) Use Hermite interpolation to find a polynomial H of lowest degree satisfying H(-1) = H'(-1) = 0, H (0) = 1, H'(0) = 0, H(1) = H' (1) = 0. Simplify your expression for H as much as possible. (b) Suppose the polynomial H obtained in (a) is used to approximate the function f(x) = [cos(Tx/2)]² on -1 ≤ x ≤ 1. i. Express the error E(x) = f(x) - H(x) (for some fixed r in [-1,1]) in terms appropriate derivative of f.