Instructor: Zhaojun Bai,
Associate Professor of Numerical Analysis and Scientific Computing
Class date and time: M.W.F. 2:00 -- 2:50, Fall 1998
Class place: CB 345
Office hour: M.W.F. 11:00 -- 12:00
Mid-term exam: Oct. 16, 2:00 - 3:00pm,
Final exam: Thursday, Dec.17, 1:00 -- 3:00 pm
Textbook
J. Demmel: Applied Numerical Linear Algebra , SIAM, 1997, homepage
Sections to be covered: 1.1 - 1.7, 2.1 - 2.4, 2.7, 3.1 - 3.5, 4.1 - 4.4, 5.1 - 5.4
Syllabus (PostScript file)
Main References
G. Golub and C. Van Loan, Matrix Computations, 3rd edition, The John Hopings Press, 1997
N. Trefethen and D. Bau, III, Numerical Linear Algebra, SIAM, 1997
E. Anderson et al, LAPACK Users' Guide, 2nd edition, SIAM, 1995
N. J. Higham, Accuracy and
Stability of Numerical Algorithms, SIAM, 1996
Lectures and Notes (all lecture notes are in plain ps files)
Lecture 1,
8/26, first day of class, syllabus, introduction
Lecture 2,
8/28, vector and matrix norms*
Lecture 3,
8/31, miscellaneous topics in linear algebra*
Lecture 4,
9/2, finite precision arithemetic
Lecture 5,
9/4, Introduction to floating point error analysis
Lectures 6 and 7,
9/9 & 9/11, Sensitivity of Linear Systems of Equations*
Lectures 8 and 9,
9/14 & 9/16, Gaussian Elimination and LU Factorization*
Lecture 10,
9/18 & 9/21, Gaussian Elimination (LU) in Finite Precision Arithmetic
Supplement of Lecture 10
Lectures 11 and 12,
9/23 & 9/25, Special Linear Systems*
Lecture 13,
9/30, Linear Least Squares Problems, basic theory*
Lecture 14,
10/5, Numerical Methods for Solving LS Problem I: Normal equation, QR decomposition*
Lecture 15,
10/7, Numerical Methods for Solving LS Problem II: Singular Value Decomposition*
Lecture 16,
10/9, Sensitivity of the Least Squares Problem
Lecture 17,
10/12, Rotation and Reflection Transformations
Supplement of Lecture 17,
Unitary Rotation and Reflection Transformations
10/14,
Review
10/16, Mid-Term Exam (one hour)
Lecture 18,
10/19, QR decomposition by Rotation and Reflection Transformations
Lecture 19,
10/21, Rank Deficient Least Squares Problems
Lecture 20,
10/23, Essentials of Matrix Eigenvalue Problems*
Lecture 21,
10/26, Power Method and Inverse Iteration*
Lecture 22,
10/30, Orthogonal iteration and QR iteration.
Lecture 23,11/2 and 11/4,
Hessenberg QR iteration with a shift and Practical QR Algorithm
Lecture 24,11/6 and 11/9,
Sensitivity (Perturbation Theory) of Eigenvalue Problems*
Lecture 25,11/11 and 11/16,
Essentials and Perturbation Theory*
Supplement
Lecture 26,11/18,
Algorithms for the SEP - I: RQI and QR*
Lecture 27,11/23,
Algorithms for the SEP - II: Jacobi's method
Lecture 28,11/25,
Algorithms for the SEP - III: Divide-and-Conquer method
Lecture 29,11/30,
Algorithms for the SEP - IV: Bisection and Inverse Iteration
Lecture 29,12/2,
Algorithms for the SVD
Lecture 31,12/4, open
Final Review I, December 15 (Tuesday), 4:00-5:00pm, CB345
Final Review II, December 16 (Wednesday), 4:00-5:00pm, CB345
Final Exam, December 17 (Thursday), 1:00 -- 3:00 pm, CB 345
Guest lecture:
Homework and Project assignments, and due date
Homework 1 ,
miscellaneous problems in linear algebra, due Sep. 10, 1998.
Computing Project 1 ,
stability and accuracy of solving linear system of equations, due Sep. 30, 1998.
Homework 2 ,
Linear system of equations, due October 14, 1998.
Homework 3 ,
Basic theory of eigenvalue problems, due November 6, 1998.
Homework 4 ,
Algorithms for general matrix eigenvalue problems, due November 23, 1998.
Computing Project 2 , Basic
algorithms for solving eigenproblems, due November 23, 1998.
Homework 5 ,
Algorithms for SEP and SVD, due December 4, 1998.
Class links
MA/CS 622, Spring 1999
Student version of Matlab
LAPACK
Offsprings of LAPACK: LAPACKin C, in C++, in Java, in Fortran 90
Where to refresh my memory of basic linear algebra
G. Strang, Introduction to linear algebra, Wellesley-Cambridge Press
or any undergraduate textbook you can get from library,
I have also collected quite few undergraduate linear algebra
textbooks, you are welcomed to stop by and borrow one.