Numerical Computation (Fall 2024)

Fudan University · Location: H6504, Handan campus · Lectures: Wed 6:30–9:05pm

Lecture 01 — Course introduction (4 Sept 2024)

notes · slides · code

• How to compute the square root of two
• Floating-point numbers and IEEE 754
• Machine epsilon and relative approximation error
• Bisection for root finding

Lecture 02 — Root finding: f(r) = 0 (11 Sept 2024)

notes · slides · code

• Bisection
• Fixed-point iteration
• Newton’s method
• Secant method
• Sensitivity analysis

Lecture 03 — Solving Ax = b (18 Sept 2024)

notes · slides

• Normed vector spaces and matrices
• Direct methods (Gaussian elimination, Cholesky factorization)
• Iterative methods (Jacobi, Gauss–Seidel, SOR)