•Let b(i) be the right-hand-side of the linear system
P(i), and x(i) an approximate
solution to P(i). Thus, x(i) and b(i) are (2^i-1)-by-(2^i-1) arrays of values at each grid
point.
•Next define operators that transfer information between grids.
–The restriction
operator R(i) takes a pair (b(i),x(i)),
consisting of a problem
P(i) and its approximate solution x(i), and maps it to (b(i-1),x(i-1)), the companion problem on the next coarser
grid. On grid (i-1),
start with a guess at the solution
x(i-1): ( b(i-1), x(i-1) ) = R(i)(
b(i), x(i) ) We will see that restriction is implemented simply by computing a weighted average of each grid point value
with its nearest neighbors.