MATH4981D Computational Linear Algebra (3 credits)
- Description: This is a concise introduction to the field of numerical linear
algebra. Topics including singular value decomposition, QR factorization,
Householder triangulation, eigenvalue problems,
their underlying principles of conditioning and stability, and introduction
to iterative methods. Students should seek instructor's approval to
take this course.
- Prerequisites: MATH 3312
- Instructor: Shingyu Leung
- Email: masyleung @ ust.hk
- Office: 3491
- Office hours:
- Lectures: Monday, Friday 630pm-730pm
- Textbook: Numerical Linear Algebra - L.N. Trefethen and D. Bau, III
Course Requirements
- Weekly presentation: students are expected to present in-turn for course materials.
- Weekly assignment: students presenting the chapter will be responsible for finishing the homework
assignments from the corresponding chapter in the textbook.
Topics
- Part I: Fundamentals
- Lecture 1: Matrix-Vector Multiplication;
- Lecture 2: Orthogonal Vectors and Matrices;
- Lecture 3: Norms;
- Lecture 4: The Singular Value Decomposition;
- Lecture 5: More on the SVD.
- Part II: QR Factorization and Least Squares.
- Lecture 6: Projectors;
- Lecture 7: QR Factorization;
- Lecture 8: Gram-Schmidt Orthogonalization;
- Lecture 9: MATLAB;
- Lecture 10: Householder Triangularization;
- Lecture 11: Least Squares Problems.
- Part III: Conditioning and Stability.
- Lecture 12: Conditioning and Condition Numbers;
- Lecture 13: Floating Point Arithmetic;
- Lecture 14: Stability;
- Lecture 15: More on Stability;
- Lecture 16: Stability of Householder Triangularization;
- Lecture 17: Stability of Back Substitution;
- Lecture 18: Conditioning of Least Squares Problems;
- Lecture 19: Stability of Least Squares Algorithms.
- Part IV: Systems of Equations.
- Lecture 20: Gaussian Elimination;
- Lecture 21: Pivoting;
- Lecture 22: Stability of Gaussian Elimination;
- Lecture 23: Cholesky Factorization.
- Part V: Eigenvalues.
- Lecture 24: Eigenvalue Problems;
- Lecture 25: Overview of Eigenvalue Algorithms;
- Lecture 26: Reduction to Hessenberg or Tridiagonal Form;
- Lecture 27: Rayleigh Quotient, Inverse Iteration;
- Lecture 28: QR Algorithm without Shifts;
- Lecture 29: QR Algorithm with Shifts;
- Lecture 30: Other Eigenvalue Algorithms;
- Lecture 31: Computing the SVD.
- Part VI: Iterative Methods.
- GMRES, CG, PCG.