Numerical Methods05 marksNumerical: Horner's method polynomial evaluationHorner's method for polynomial evaluation
Define the terms true error and relative error? Write down algorithm for Horner' method to evaluate polynomial and use the method to evaluate the polynomial 2x3 - 3x2 + 5x - 2 at x=3.
Define the terms true error and relative error? Write down algorithm for Horner' method to evaluate polynomial and use the method to evaluate the polynomial $2x^3 - 3x^2 + 5x - 2$ at x=3. [5]
- Polynomial: $P(x) = 2x^3 - 3x^2 + 5x - 2$ - Coefficients (high to low degree): $a3 = 2,\ a2 = -3,\ a1 = 5,\ a0 = -2$ - Evaluation point: $x = 3$ The true error is the difference between the exact (true) value and the approximate (computed) value. $$Et = X{\text{true}} - X{\text{approx}}$$ It ex...