3. (a) Use Hermite interpolation to find a polynomial H of lowest degree satisfying H(-1)= H'(-1) = 0, H (0) = 1, H'(0)

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3 A Use Hermite Interpolation To Find A Polynomial H Of Lowest Degree Satisfying H 1 H 1 0 H 0 1 H 0 1 (123.24 KiB) Viewed 19 times

3. (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. 11 i. Express the error E(x) = f(x) - H(x) (for some fixed x in [-1,1]) in terms o appropriate derivative of f. ii. Estimate max-1<<1 E(x).