Numerical Analysis 1

Fall 2025

Course logistics, policies, content

Homework assignments now including Homework 5.

Day 01, Aug 26: Outline, photos and screenshots. What is numerical analysis? What is this course about? Machine numbers.

Day 02, Aug 28. More detail about floating-point machine numbers, and starting to think about machine arithmetic.

Day 03, Sep 2. Relative error in floating point arithmetics, and some remedies.

Day 04, Sep 4. Roundoff error bound. Root-finding 1D: bisection, functional iteration.

Day 05, Sep 9. Conditions for convergence of functional iteration to a fixed point, convergence with order q.

Day 06, Sep 11. Newton failure. Secant method. Stopping criteria. Linear systems.

Day 07, Sep 16. Implementation of GE and BS. Speed of computer arithmetic. Operation count for GE.

Day 08, Sep 18. Vectorization. GE with partial pivoting. Round-off in GE. Bound on change in solution when problem perturbed.

Day 09, Sep 23. GE as LU factorization. Overdetermined systems and QR factorization.

Day 10, Sep 25. QR factorization cont'd, implementation. Application of QR.

Day 11, Sep 30. Exam 1

Day 12, Oct 2. Concluding notes on QR. Ch 4. Polynomial approximation: Weierstrass theorem, Bernstein polynomials.

Day 13, Oct 7. Polynomial interpolation, using Lagrange and monomial bases. (Jupyter notebook)

Day 14, Oct 9. Error bound for polynomial interpolation. Piecewise polynomial interpolation (linear and cubic).