Text book: Numerical Analysis, Richard L. Burden and J. Douglas Faires, 10th edition

Mathematical preliminaries and error analysis (slide, 2020spring_print, 2020spring)

• Round-off errors and computer arithmetic

1. IEEE standard floating-point format (video)

2. Absolute and relative errors (video)

3. Machine epsilon

4. Loss of significance (video)

• Algorithms and convergence (video)

1. Algorithm

2. Stability

3. Rate of convergence

Hand-son programming

Solutions of Equations in One Variable (slide, 2019fall, 2019fall_print)

• Bisection Method (video)

• Fixed-point iteration (video)

• Newton’s method (video)

• Error analysis for iterative methods (video1), (video2)

• Accelerating convergence

• Zeros of polynomials and Muller’s method (video)

Hands-on programming

Direct Methods for Solving Linear Systems (slide, 2019fall, print)

• Linear systems for equations (video1), (video2)

• Pivoting Strategies (video)

• Matrix factorization (video1), (video2)

• Special types of matrices (video1), (video2)

Iterative techniques in matrix algebra (slide, 2018spring, print)

• Norms of vectors and matrices (video)

• Eigenvalues and eigenvectors

• Jacobi and Gauss-Siedel Iterative Techniques (video1), (video2)

• Relaxation Techniques for Solving Linear Systems (video)

• Error bounds and iterative refinement (video)

• Conjugate gradient method (video1), (video2), (video3), (video4)