MA428

MA/CSC 428-001: Numerical Analysis II

Spring Semester, 2024

Time: T TH, 1:30-2:45 pm Place: SAS 2229
Instructor: Dr. Zhilin Li Office: SAS 3148, Tel: 919-515-3210
E-mail: zhilin@ncsu.edu Office hours: T TH 10:30-11:20am, or by appointment

Due to the corona virus pandemic, public health measures have been implemented across campus. Students should stay current with these practices and expectations through the Protect the Pack website (https://www.ncsu.edu/coronavirus/). Face masks are optional. Consideration and understanding for wearing masks or not wearing masks are both appreciated.

Classes Notes will be available on Moodle.

Goals and Objectives:

This course is designed for students in engineering, physical and mathematical sciences. The course covers most of materials in numerical linear algebra. We will address issues of algorithm development, implementation and applicability, the error analysis including effect of round off errors, available software packages, and parallel computing to some extent. Main topics include: direct and iterative methods for solving system of linear equations, least squares solutions, eigenvalues problem, singular value decomposition, and non-linear system of equations.

Textbook:

Notes from the instructor.

Numerical Algorithms, by Justin Solomon, free available on Moodle and on the Internet

Numerical Analysis, by Timothy Sauer, any edition

A summary of basics of Linear Algebra

Prerequisites:

A reasonable background in calculus, linear algebra. Some programming experiences are helpful, but not essential.

Grading:

Homework (analytic part and computer projects) including some class practices: 70%; Final exam: 30%.

Up to 5% extra credits for group works (3-4 in a group), and active class participation.

Computing:

Matlab: will be used for instructions and is recommended for homework. However, you can use Python, C, C++, Fortran, or other computer language and software packages as well.

Matlab_tips

Materials:

Introduction: Linear algebra review

Direct methods for linear systems, Gaussian elimination, LU, PLU, LL' decomposition.

Iterative methods for linear systems, Jacobi, Gauss-Seidel, SOR, Spectral radius, Krylov methods, CG and PCG, GMRES.

Eigenvalues problems and computation, eigenvalues estimation, Power and shifted Power method, orthogonal transformation, QR algorithm

Least squares and SVD decomposition and solutions

Nonlinear least squares solution and non-linear system of equations

Other References:

Matrix Computations, G. Golub and C. F Van Loan, John Hopkins

Tacoma Bridge Collapse: 1940 Explanation: 1. Oscillation of bridge caused by the wind frequency being too close to the natural frequency of the bridge 2. Natural frequency of thebridge is the eigenvalue of the smallest magnitude (based on a system that modeled the bridge)

Computing Resources:

MATLAB help at Utah
MATLAB Primer: A good staring point for learning MATLAB. Math-Works Link.
Matlab Guide: Second Edition, SIAM, 2005, Desmond J. Higham and Nicholas J. Higham.

Matlab Codes:

quad_err.m deri.m drive1.m my_fun.m	my_gauss.m drive_GE.m my_gauss_pp.m my_cholA.m my_hilbert.m my_LU_drive.m my_LU_solver.m my_Crout.m
interpolation.m my_sor.m sor_drive.m	Two_Point_SOR poisson_drive.m poisson_sor.m
cond_hw.m	my_power.m my_power_shift.m my_qr_eig.m

CG_Test.m GMRES_Matlab_Test.m
gmres_drive.m my_gmres.m atv.m givapp.m bc.m u1d_to_2d.m u2d_to_1d.m

Calendar:

Calendar

Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  
                                   1  2  3                  1  2  
    B  9 10 11 12 13   4  5  6  7  8  9 10   3  4  5  6  7  8  9  
14  H 16 17 18 19 20  11 12  W 14 15 16 17  10  B  R  E  A  K 16  
21 22 23 24 25 26 27  18 19 20 21 22 23 24  17 18 19 20 21 22 23  
28 29 30 31           25 26 27 28 29        24 25 26 27 28 29 30  
                                            31                    

       April                  May                   June          
Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  Su Mo Tu We Th Fr Sa  
    1  2  3  4  5  6            1  2  3  4                     1  
 7  8  9 10 11 12 13   5  6  7  8  9 10 11   2  3  4  5  6  7  8  
14 15 16 17 18 19 20  12 13 14 15 16 17 18   9 10 11 12 13 14 15  
21 22  L 24  F 26 27  19 20 21 22 23 24 25  16 17 18 19 20 21 22  
28 29 30              26 27 28 29 30 31