ma580_logo MA/CSC 580-001: Numerical Analysis

Fall Semester, 2019

clockCourse Outline



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:

Homework  (analytic part and computer projects):  65%;  A Take-Home Test: 35%.
Class participation:        + or -    3% (excessive absences will affect the grade linearly)


HOMEWORK   ( Moodle via Wolfware )        Guidelines

HW1       
HW2
HW3          
  HW 4         Soln
HW5 


Notes:   Matlab_tip

Week 1 (8/22),   Week 2 (8/29)Week 3 (9/5), Week 4 (9/12), Week 5 (9/19), Week 6 (9/26), Week 7 (10/5),  Week 8 (10/3), Week 9 (10/10),

Week 10 (10/17), Week 11 (10/24),  Week 12 (10/31), Week 13 (11/7), Week 14 (11/14), Week 15 (11/21)Week 16 (11/28),  Week 17 (12/5)


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:

        Two_Point_SOR  

    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:

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

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

    M: Midterm Exam;   F: