Numerical Linear Algebra (Fall 2023)
Prerequisites:   Mathematical Analysis, Advanced Algebra, Matlab Programming
Highlights:   专业核心课程,深入探讨数值线性代数
Classroom quizzes:
Quiz I (Lectures 1 – 4), 2023年10月30日星期一10:00 – 12:00,海韵教学楼201
Quiz II (Lectures 5 – 10), 2023年12月11日星期一10:00 – 12:00,海韵教学楼201
Final exam (Lectures 1 – 12), 2024年1月2日星期二10:30 – 12:30,海韵教学楼202
Grading Policy: Assignments 30% + Classroom quizzes 20% + Final exam 50%
Instructor
References
Numerical Linear Algebra (NLA), Lloyd N. Trefethen and David Bau, III, SIAM, 1997. Twenty-fifth Anniversary Edition, 2022
Applied Numerical Linear Algebra (ANLA), James Demmel, SIAM, 1997
Matrix Analysis and Applied Linear Algebra (MAALA), Study and Solutions Guide, Carl D. Meyer, 2nd Edition, SIAM, 2023
Numerical Linear Algebra An Introduction (NLAI), Holger Wendland, Cambridge University Press, 2018
Iterative Methods and Preconditioners for Systems of Linear Equations (IMPSLE), Gabriele Ciaramella and Martin J. Gander, SIAM, 2022
数值线性代数, 徐树方, 高立, 张平文, 第二版, 北京大学出版社, 2013
数值线性代数, 曹志浩, 复旦大学出版社, 1996
MathWorks MATLAB 帮助中心
Lecture Notes
Lecture 1: Inner product, Orthogonality, Vector/Matrix norms.
Lecture 2: Singular value decomposition (SVD).
Lecture 3: Projector, Classical/Modified Gram–Schmidt orthogonalization, QR factorization.
Lecture 4: Householder reflector, Givens rotation, Least squares problem.
Lecture 5: LU factorization, Cholesky factorization, Gaussian elimination with pivoting.
Lecture 6: Stationary iterative methods.
Lecture 7: Eigenvalue problem.
Lecture 8: Power/Inverse iteration, Rayleigh quotient iteration.
Lecture 9: QR algorithm.
Lecture 10: Jacobi method, Bisection method, Divide-and-conquer method.
Lecture 11: Krylov subspace, Generalized minimal residual method.
Lecture 12: Conjugate gradients.    (Proof of Theorem 1)
Lecture 13: Biorthogonalization methods.
Lecture 14: Krylov subspace methods for least squares problems.
Lecture 15: Krylov subspace methods for eigenvalue problems.
Lecture 16: From Lanczos to Gauss quadrature.
Lecture 17: FFT and structured matrices.
Lecture 18: Multigrid.
Lecture 19: Conditioning of a problem.
Lecture 20: Backward stability of an algorithm.
Assignments
Other
The Matrix Cookbook, Kaare Brandt Petersen and Michael Syskind Pedersen
矩阵求导术(上), 矩阵求导术(下)
The Singular Value Decomposition, Applications and Beyond, Zhihua Zhang, arXiv:1510.08532, 2015
Image Compression with Singular Value Decomposition, Tim Baumann
The History of Numerical Analysis and Scientific Computing, SIAM
Branches of Mathematics: Numerical analysis, Lloyd N. Trefethen, Princeton U. Press, 2008.
矩阵计算 / 数值线性代数, 华东师范大学, 潘建瑜
Matrix Computations / Numerical Linear Algebra, U.C. Berkeley, James Demmel
Computational Aspects of Matrix Theory, University of Minnesota, Yousef Saad
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