Question

Which of these creates a problem in Newton’s method for solving non-linear system of equations?

(a) Taylor series

(b) Jacobian

(c) Convergence

(d) Speed

This question was posed to me during an internship interview.

My query is from Numerical Methods in division Numerical Methods of Computational Fluid Dynamics

Answer 1

The correct choice is (b) Jacobian

The best explanation: At each iteration of Newton’s method, Jacobian has to be evaluated for the method to be effective. Evaluation of the Jacobian with n^2 elements at each step will be expensive. Moreover, a direct method of evaluating the Jacobian does not exist.