Numerical Linear Algebra
This course is a core course for graduate students in computational mathematics and an elective for graduate students and senior undergraduates in other mathematics disciplines, as well as in mechanics, computer science, and related fields. It covers numerical methods for solving linear equations, least squares problems, and eigenvalue problems, including algorithms such as QR decomposition, LU factorization, Krylov subspace methods, and preconditioning techniques. Emphasis is placed on numerical stability and error analysis, highlighting the role of sparse matrix structures in engineering and scientific computing. In the context of developments in artificial intelligence (AI) and high-performance computing (HPC), the course introduces cutting-edge applications of numerical linear algebra. Upon completion, students are expected to master fundamental methods in numerical linear algebra, acquire a solid understanding of the latest developments in matrix computations, and appreciate the critical role of linear algebra in scientific and engineering calculations.
Lecture Time: M, W 13:30--15:05 (5 min break)
Location: 国科大雁栖湖校区
Schedule:
- Chapter 1: Introduction and Applications (From 03/02/2026)
- Chapter 2: Fundamentals of Linear Algebra
- Chapter 3: Basics of Matrix Computations
- Chapter 4: Direct Methods for Linear Systems
- Chapter 5: Iterative Methods for Linear Systems
- Chapter 6: Numerical Methods for Least Squares Problems
- Chapter 7: Krylov subspace methods
- Chapter 8: Numerical Methods for Eigenvalue Problems
- Course Summary
Lecture Notes (TBA)