1. Introduction to Scientific Computing II
Institut für
Informatik
Scientific Computing
In Computer Science
Introduction to Scientific Computing II
Conjugate Gradient Method
Dr. Miriam Mehl

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

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

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