1. ANSWER THE FOLLOWING BRIEFLY BUT COMPREHENSIVELY.
What are the advantages and disadvantages of using numerical methods?
In numerical analysis, why do we need to measure error and efficiency?
Explain the difference between polynomial interpolation and splines.
What is the advantage of using parametric curves?
What are the advantages of using rational function interpolation and trigonometric interpolation?
Differentiate interpolation from least-squares approximation.
What is the importance of using Chebyshev nodes in polynomial interpolation? Can we use Chebyshev nodes if we do not know the original function to be approximated?
Differentiate l1, l2 and l∞ approximations.
What is the importance of Richardson Extrapolation?
Enumerate the differences of the following methods: Monte-Carlo integration, Closed Newton-Cotes quadrature, Open Newton-Cotes quadrature, Adaptive quadrature and Gaussian quadrature.