High Performance Computing 1
R(i)
•Thus, P(i-1) will be the problem of solving T(i-1)*d(i-1) = r(i-1), for the correction d(i-1), starting with the initial guess x(i-1) of all zeros.
•The restriction will be accomplished by averaging nearest neighbors of r(i) on the fine grid (with 2^i-1 unknowns) to get an approximation on the coarse grid (with 2^(i-1)-1 unknowns): The value at a coarse grid point is .5 times the value at the corresponding fine grid point, plus .25 times each of the fine grid point neighbors.