Numerical Computation (Fall 2024)

Fudan University, Fall 2024

Location: H6504, Handan

Lectures: 6:30pm-9:05pm Wed.,

Lecture 01, 09-04-2024, Course Introduction (notes, slides, codes)

• How to calculate \(\sqrt{2}\)

• Float-point numbers and IEEE 754

• Machine epsilon and relative approximation error

• Bisection for root finding

Lecture 02, 09-11-2024, Root-finding (\(f(r)=0\)) (notes, slides, codes)

• Bisection

• Fix-point iteration

• Newton's method

• Secant method

• Others and sensibility analysis

Lecture 03, 09-18-2024, Solving \(\boldsymbol{A x} = \boldsymbol{b}\) (notes, slides, codes)

• Basics for normed vector spaces and matrices

• Direct methods (GE, Cholesky Factorization)

• Iteration methods (Jacobi, Gauss-Seidel, SOR)