a Polynomial interpolation and root finding problem. Consider a 6-th order polynomial f(1) =0.11.26 -0.01.25 – 0.233.24

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A Polynomial Interpolation And Root Finding Problem Consider A 6 Th Order Polynomial F 1 0 11 26 0 01 25 0 233 24 1 (42.79 KiB) Viewed 28 times

a Polynomial interpolation and root finding problem. Consider a 6-th order polynomial f(1) =0.11.26 -0.01.25 – 0.233.24 -0.01.23 – 2? + V2.2 (1) and finish the following tasks: (a) Choose a polynomial interpolation method to approximate f(x) in domain (-2.5, 2.5] and compare it with the exact function plot. (b) How many real roots does f(x) = 0 have? (c) Use an arbitrary root finding algorithm to find all real zeros of f(x). (d) Reformulate the root finding problem into a fixed-point iteration problem and then use the fixed-point theorem (Theorem 2.4 in Page 62) to determine whether the iteration converges within the neighbourhood of each root.