Week 6
Linear systems
Roundoff, pivoting, and accuracy
Reading: Golub & Van Loan §3.3–3.5, pp. 122–144.
By the end of this week you should be able to
- Explain the role of the growth factor in the stability of Gaussian elimination.
- Contrast partial and complete pivoting.
- Improve a computed solution by iterative refinement.
Algorithms introduced
- Gaussian elimination with partial pivoting
- Iterative refinement
- Condition estimation
Where this shows up in AI
Every library solver pivots. Knowing what breaks without it is the difference between trusting a result and merely obtaining one.
Materials
- Slides
posted before class - Notes
posted after class - Code
to be added - Due this week
nothing due