MATH 504: Numerical Linear Algebra

• Numerical Linear Algebra, by Trefethen and Bau SIAM
• Matrix Computations, by Golub and Van Loan John Hopkins
• Iterative Methods for Linear and Nonlinear Equations, by C. T. Kelley Free PDF at SIAM

• Applied Numerical Linear Algebra, by Demmel SIAM
• Linear Algebra and Its Applications, by Strang Amazon

Course Description:   Direct and iterative methods of the solution of linear systems of equations and least squares problems. Error analysis and numerical stability. The eigenvalue problem. Descent methods for function minimization, time permitting. For each algorithm we investigate its efficiency, stability and accuracy. Efficient implementation of common algorithms in Numerical Linear Algebra and analysis of the effects of finite precision on stability. Master proof techniques commonly used in numerical linear alegebra (and numerical analysis in general).

Syllabus  

Computation You can use either Python, Matlab or C/C++ for the computations.

*Python

I find Python along with the libraries numpy, scipy and matplotlib better than Matlab. Python has a very gentle learning curve, so you should feel at home even if you've never done any work in Python.

*Python and Numpy Help

• Python tutorial (https://docs.python.org/3/tutorial/index.html)
• Facts and myths about Python names and values (http://nedbatchelder.com/text/names.html)
• Dive into Python 3 (http://www.diveinto.org/python3/)
• Introduction to Python for Science (https://github.com/djpine/pyman)
• The SciPy lectures (http://scipy­lectures.github.io/)
• The Numpy MedKit (http://mentat.za.net/numpy/numpy_advanced_slides/)
• The Numpy User Guide (http://web.mit.edu/dvp/Public/numpybook.pdf) by Travis Oliphant
• Spyder (https://github.com/spyder­ide/spyder) (a Python IDE, like Matlab)
• An introduction to Numpy and SciPy (http://www.engr.ucsb.edu/~shell/che210d/numpy.pdf)
• 100 Numpy exercises (http://www.loria.fr/~rougier/teaching/numpy.100/index.html)

*Matlab

A simple tutorial (intended for Math 375) MATLAB tutorial (PDF) script with all commands(matlab_tutorial.m) ApproxExp.m f1.m df1.m MyDeriv.m my_funky_fcn.m

MTU

MIT

*C/C++

C/C++ is like a double shot espresso. If you don't know what it is, its better to steer clear.

Grading:  

60-70% Homework
0-10% Class Participation
30% Exams (10% for Midterm + 20% for Final)

Weights: Maximum of

• 70% HW + 30% Exams
• 60% HW + 10% Participation + 30% Exams

After the above weighted score has been calculated, letter grades will be assigned according to the following scheme: A, 90 or above, B, 80 or above, C, 70 or above, D, 60 or above, F below 60. However, the instructor reserves the right to “curve” grades to offset unforeseen circumstances. The curving of grades will never decrease a student’s letter grade below that given by the above formula.

Important Dates:  
Midterm Exam :   March 2 (Thursday), in Class
Final Exam:   May 9 (Tuesday), 7:30 am - 9:30 am (Ouch!)

Notes Week 1  Week 2  Week 3  Week 4  Weeks-5-6  Week-7  lost count 1  lost count 2  Eigenvalues  Classical Iterative Solvers  CG  GMRES etc  Remaining Items 

Homeworks: The homeworks will have both a computational and theoretical component. Late homeworks will not be accepted.
Computational Exercises
Homework 1 (Already!?)
Homework 2
Homework 3
Homework 4 and 5
Homework 6
Homework 7   hw7_svd.m
Homework 8  
Homework 9  
Homework 10  
Homework 11   generate_2d_poisson_mat_rhs.m