•Here we consider a so-called weighted Jacobi smoothing operator S(i).
•Pure Jacobi would replace the j-th component of the approximate solution x(i) by the weighted average:
•x(i)(j) = .5*( x(i)(j-1) + x(i)(j+1)
+ 4^i * b(i)(j) )
• = x(i)(j) + .5*( x(i)(j-1) -
2*x(i)(j) + x(i)(j+1)
• + 4^i * b(i)(j) )
•Weighted Jacobi instead uses
•x(i)(j) = x(i)(j) + w*.5*(
x(i)(j-1) - 2*x(i)(j) + x(i)(j+1)
• + 4^i * b(i)(j) )
•