•The restriction
operator R(i) takes a problem P(i) with
right-hand-side b(i)
and an approximate solution x(i), and maps it to a simpler problem P(i-1) with right-hand-side
b(i-1) and approximate
solution x(i-1).
•Let r(i) be the residual of the approximate solution x(i):
• r(i) = T(i)*x(i) - b(i)
•If x(i) were the exact solution, r(i) would be zero.
•If we could solve the equation T(i) * d(i) = r(i)
exactly for the correction
d(i), then x(i)-d(i) would be the solution we seek, because
• T(i) * ( x(i)-d(i) ) = T(i)*x(i) -
T(i)*d(i)
• = (r(i)
+ b(i)) - (r(i)) = b(i)