Question

Consider the global matrix AΦ=b. What is the residual at the ith iteration? (Note: Φi is the value of Φ in the i^th iteration).

(a) AΦ^i-1+b

(b) AΦ^i-1-b

(c) AΦ^i+b

(d) AΦ^i-b

The question was posed to me in exam.

I want to ask this question from Numerical Methods in portion Numerical Methods of Computational Fluid Dynamics

Answer 1

Correct option is (d) AΦ^i-b

To explain: While solving the system AΦ=b, AΦ-b should be equal to zero. Since, the iterative method will not produce such an answer, the decision when to stop the iteration relies upon a tolerance value. When the residual AΦ^i-b becomes less than the tolerance, iterations are stopped.