Relaxation Scheme for system Au=f
I'm trying to answer this question, but am completely stuck.
Argue that in analyzing the error in a stationery linear relaxation scheme applied to , it is sufficient to consider with arbitrary initial guess, (say ).
I'm not even sure what the author is trying to say, is he saying when studying the error produced by the relaxation method (eg. the jacobi method) it is sufficient to study the error of the associated homogenous system with arbitrary initial guesses (say ). But in this case the error will simply be . (since the error is defined as )
Maybe the residual equation plays a part, ... ???
Any help, would be much appreciated