Sma 2321 numerical analysis assignment - define the

Question

Numerical Analysis Assignment -

Q1. Define the following terms:

(i) Truncation error

(ii) Round-off error

Q2. Show that if f(x) = logx, then the condition number, c(x) = |1/logx|. Hence show that log x is ill-conditioned near x = 1.

Q3. If x = 2.536, find the absolute and relative error when,

(i) x is rounded off to 2 decimal places, and

(ii) is truncated to 2 digits.

Q4. Show that the square root of a number N is given by x_n+1 = ½{x_n + (n/x_n)} and use it to find √(11.4) correct to 6 decimal places, taking x₀ = 3.5.

Q5. Use Horner's method to compute p(3) where p(x) = x⁵ - 6x⁴ + 8x³ + 8x² + 4x - 40. Hence write p(x) in the form P(x) = (x - α)Q(x) + R_n.

Q6. Using Newton-Raphson method find the root α ∈ [1, 2] of log x - cos x = 0 correct to 2 decimal places.