Matrix Computations and Applications (Spring 2011)

[ Time: Mons, 3:55pm-5:30pm; Thurs, 6:30pm-8:05pm || Place: West Cao Building 101 ]

[ TA: Gao Cuixia, cuixiagao0209@gmail.com ]

Contents

  • Lecture 1 Matrix Problems in Machine Learning: Page Rank & Google Matrix, PCA, PCO, MDS and FLDA. (PDF)

  • Lecture 2 Matrix Fundamentals. (PDF) (PDF)

  • Lecture 3 Norms for Vectors and Matrices. (PDF)

  • Lecture 4 Singular Value Decomposition and Applications. (PDF) (PDF) (PDF)

  • Lecture 5 QR Decomposition and Applications. (PDF)

  • Lecture 6 LU Factorization and Choleskey Factorization, with Applications in Gaussian Elimination for Linear Equation Solving. (PDF)

  • Lecture 7 Eigenvalue Problems. (PDF) (PDF)

  • Lecture 8 Iterative Methods for Linear Systems: Jacobi, Gauss-Seidel and Successive Overrelaxation; General Convergence Result, Regular Splittings, Diagonally Dominant Matrices, Gershgorin's Theorem; General Descent Methods, the Steepest Descent Algorithm, the Conjugate Gradient Algorithm.

    • Homework

  • Homework 1 (PDF) (Sol1)

  • Homework 2 (PDF) (Sol2)

  • Homework 3 (PDF) (Sol3)

  • Homework 4 (PDF)

    • Textbooks

  • Lloyd N. Thefethen and David. Bau, III. Numerical Linear Algebra. SIAM, Philadelphia, 1997.

  • Gene H. Golub and Charles F. Van Loan. Matrix Computations (Third Edition). The Johns Hopkins University Press, Baltimore, 1996.

    • Reading Lists

  • Lloyd N. Thefethen. The definition of numerical analysis, SIAM News, Nov 1992. (PDF)