Question

Consider the global matrix AΦ=b. Let the coefficient matrix A=M-N. At the i^th iteration, the general form can be given as ______________ (Note: Φ^i is the value of Φ in the i^th iteration).

(a) MΦ^i=NΦ^i-1+b

(b) MΦ^i=NΦ^i+b

(c) MΦ^i=NΦ^i-1-b

(d) MΦ^i=NΦ^i-b

Answer 1

Right option is (a) MΦ^i=NΦ^i-1+b

The best I can explain: The global matrix is

AΦ=b

Replacing A with M-N,

(M-N)Φ=b

MΦ=NΦ+b

At a particular step, we only know the Φ values of the previous step only. So,

MΦ^i=NΦ^i-1+b.