Intuitive Description of Poor Person's Conjugate Gradient Algorithm

• So Poor Person's Conjugate Gradient is very good at large eigenvalues, but converges slowly for small eigenvalues of A.

• Note A is positive definite for simple pde's .

• What we would like to do is to arrange first that , then we see that equations give , and then the next iteration will give , and so on.

• So qualitative goal of real conjugate gradient is to successively minimize along the ``principal directions of matrix A.''

• As described in my optimization notes, this is easily understood in case n=2 in terms moving in hills and valleys.