Numerical linear algebra, Skoltech, Fall 2016, general course info.

Lecture access

Lectures can be downloaded and viewed on github: https://github.com/oseledets/nla2016
They can also be viewed online using nbviewer: http://nbviewer.jupyter.org/github/oseledets/nla2016/tree/master/

The most comfortable way to navigate through course materials is to use table_of_contents.ipynb file in repo.

Team

Ivan Oseledets, i.oseledets@skoltech.ru,
Maxim Rakhuba, m.rakhuba@skoltech.ru,
Marina Munkhoeva, marina.munkhoeva@skolkovotech.ru,
Alexandr Katrutsa, aleksandr.katrutsa@phystech.edu.
Artem Nikitin,
Valentin Khrulkov

Feedback system

We encourage you to use Piazza platform for communication with TAs and with each other.

How do we grade

40% homework. Includes 3 problem sets with coding in Python and theoretical problems.
15% written midterm test (previous year tests are here: v1 and v2)
15% final oral exam in the traditional manner of Russian oral exams.
30% term project. We encourage that you suggest your own term project. Team should be 3-4 people. On Piazza you will find more info and you can use it to find teammates.

Deadlines & attendance & late submissions

Strict deadlines. 2 days after deadline gives 80% maximum. Then 50%.
No penalties for absense, but we will collect attendance lists each lection for statistics.

Course description

Numerical linear algebra is the basis for computational science and engineering and data science
Matrices and their decompositions are the key
The tools are different for small-scale and large-scale problems

Learning outcomes

Solve medium-scale numerical linear algebra problems (solve linear systems, compute eigenvalues and eigenvectors, solve linear least squares) using matrix factorizations
Iterative methods for sparse/structured systems
Find which methods are the most appropriate for the particular problem
Find appropriate software

Some details

We will use Python ecosystem for programming. The first week we will spend for the Python crash course (including today)
All the homework will be distributed in the form of Jupyter notebooks



In [4]:

    
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
import seaborn  as sns
x = np.linspace(0,1,1024)
plt.plot(np.sin(20*x))
#Do some random plot here









    Out[4]:





[<matplotlib.lines.Line2D at 0x110308050>]

(Approximate) Syllabus

Week 1: Floating points arithmetics, matrices, vectors, norms, ranks
Week 2: Matrix decompositions 1: SVD and its applications
Week 3: Matrix decompositions 2: Linear systems and LU, eigendecomposition
Week 4: Matrix decompositions 3: QR and Schur + test
Week 5: Sparse and structured matrices, iterative methods, preconditioners
Week 6: Matrix functions and advanced topics (compressed sensing, tensor decompositions)
Week 7: Oral exam
Week 8: Application period

From advanced topics, we will try to cover compressed sensing, image procession and tensor factorizations.

Books

Golub, Van Loan, "Matrix computations" (4th edition)
Tyrtyshnikov, "Brief introduction to numerical analysis"
Demmel, "Numerical Linear Algebra"

Coding & Python

If there is a request, we can organize a short Python/Numpy/Jupyter tutorial.



In [1]:

    
from IPython.core.display import HTML
def css_styling():
    styles = open("./styles/custom.css", "r").read()
    return HTML(styles)
css_styling()









    Out[1]: