Solution found by an iterative procedure: first guess x0 →A x0 + b
= r0 ≠0
1.4
x ii-th approximation
vector A. xi+ b = ri, i-th residual vector i = 0,1,2,3,......,m ri = grad f(xi) gradient, the error in the energy norm f(xi) = ½ xi*A xi+b*xi
For solving
such a systemone starts out with a
first guess.
The notion of
residual vector is then introduced. It gives toa certain extent a measure for how far one is from the solution
of the problem.
This initial
guess is then step by step improved, which leads to a new approximation
vector.