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