1. Introduction to Scientific Computing II
Conjugate Gradient Method
Dr. Miriam Mehl

2. Steepest Descent – Convergence
Poisson with 5-point-stencil
like Jacobi

3. Steepest Descent – Convergence

4. Conjugate Gradients – Basic Idea
solution of SLE
minimization
iterative
one-dimensional minima
no repeating search directions

5. Steepest Descent – Principle

6. Conjugate Gradients – Principle

7. CG – Algorithm

8. Steepest Descent – Example
initial error
after 1 iteration
after 10 iterations

9. Conjugate Gradients – Example
initial error
after 1 iteration
after 10 iterations

10. Conjugate Gradients – Example
Error after 50 iterations
(h=1/128)

11. Conjugate Gradients – Example
322
157 76 35
iterations cg
1/128
1/64
1/32
1/16 h
48,629
11,576
2,744
646
iterations sd
16,129
3,969
961
225
#unknowns

12. CG – Convergence Poisson with 5-point-stencil like SOR
no parameter adjustment