Jacobi Iteration into Gauss-Seidel for Linear Algebra course

Hello I have been try to write a program for a gauss-Seidel iteration on matlab but am having trouble... I have figured out how to write a Jacobi iteration program but have no idea how to convert it into Gauss-Seidel. I believe i need a new xvalue, xnew? Can anybody please help me out

Answer 1

[Matt Tearle]

Your loop in j is effectively 1:(i-1) then (i+1):n. The difference between GS and Jacobi is whether you use x or xold in that first loop.

Also note that your line x(i) = sum/a(i,i) doesn't depend on j, so it doesn't need to be in the loop (over j).

(Also don't use sum as a variable name. But that has no bearing on the GS-vs-Jacobi issue.)

[Sullman]

i have xold=x

should i change that and have a new x

[Matt Tearle]

Your code has disappeared, so it's hard to say for sure, but probably not. x should be the new x you're calculating; I'm assuming "xold = x" occurs at the beginning of the iteration. Then your Jacobi program updates x based entirely on xold. That means you're always using the previous iteration's values of x (xold). The only difference between Jacobi and GS is that GS uses the current iteration's values of x that have been computed so far. As I said, for the ith element, the x values that have been updated so far are j = 1:(i-1). So for that loop, update x(i) based on x(j). From then on (j = (i+1):n) update x(i) based on xold(j).