ma580_logo MA/CSC 580-001: Numerical Analysis

Fall Semester, 2018

clockCourse Outline

Test 1: Friday, 9/21,   Soln   Review             Test 2 :  10/29.   Review 2         Test 3

Make-up Class Dates: 11/7

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: e-Books at NCSU: 
Prerequisites:
A reasonable background in calculus, linear algebra. Some programming experiences are helpful, but not essential.

Grading: two options: choose only one (decide by 10/8)

Option1: Homework  (analytic part and computer projects):  35%;  3 Midterms: 45% (can be take-home); No make-up tests. Final: 20%.
Option2: Homework  (analytic part and computer projects):  40%;  3 Midterms: 60% (can be take-home). No make-up tests.
Class participation:        + or -    3% (excessive absences will affect the grade linearly)

HOMEWORK   ( Moodle via Wolfware )        Guidelines
HW1     hw1.tex   zmacros.tex
HW2     hw2.tex
 HW 3    hw3.tex          
HW 4       hw4.tex             
  HW 5     hw5.tex         
HW 6       hw6.tex      HW 7 (suggested)

Notes:   Matlab_tip

Week 1 (8/24),   Week 2 (8/31),   Week 3 (9/7),   Week 4 (9/14),   Week 5 (9/21),   Week 6 (9/27),   Week 7 (10/3),   Week 8 (10/12),

Week 9 (10/19),   Week 10 (10/26),  Week 11 (11/2),   Week 12 (11/9),  Week 13 (11/16),  Week 14 (11/19),   Week 15 (11/30),  Week 16 (12/7)

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.

Materials:

  • Introduction: Model problems, round off errors, norms, condition numbers.
  • Direct methods for linear systems,  Pivoting, LU, LL' decomposition.
  • Iterative methods for linear systems, Jacobi, Gauss-Seidel, SOR, Spectral radius,  Krylov methods, CG and PCG, GMRES.
  • Iterative methods for non-linear systems, Newton method and variations, Broyden method.
  • Eigenvalues and other problems in numerical linear algebra, Eigenvalues estimation, Power and shifted Power method, Orthogonal transformation, QR algorithm, Least squares solution, SVD decomposition.

    • Other References:

  • Iterative Methods for Linear and Nonlinear Equations, C.T. Kelley, SIAM
  • Numerical Analysis, Fifth Edition,  R. L. Burden and J. D. Faires, PWS-Kent Publishing Company, (under-graduate textbook)
  • Numerical Matrix Analysis, I. Ipsen, SIAM.
  • Matrix Computations, G. Golub and C. F Van Loan, John Hopkins
  • A link to significant digits.
  • 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 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
    interpolation.m     my_sor.m     sor_drive.m 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:

            July                 August              September        
    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  7            1  2  3  4                     1  
     8  9 10 11 12 13 14   5  6  7  8  9 10 11   2  H  4  5  6  7  8  
    15 16 17 18 19 20 21  12 13 14 15 16 17 18   9 10 11 12 13 14 15  
    22 23 24 25 26 27 28  19 20 21  B 23 24 25  16 17 18  D 20 M1 22  
    29 30 31              26 27 28 29 30 31     23 24 25 26 27 28 29  
                                                30                    

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

                                            
    H: Holiday, V: Vacation(No class);  L: Last day of instruction
    M: Midterm Exam;   F: