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Numerical linear algebra, Skoltech, Fall 2014, general course info.

Team

Ivan Oseledets, Associate Professor, Skoltech
Maxim Rakhuba, TA
Denis Kolesnikov, TA
Evgeny Frolov, TA

How do we grade

50% homework
50% 2 written tests
pass-fail ping-pong test

Strict deadlines
Attendance control not strict (although do not disappoint us)

Course description

Numerical linear algebra is the basis for all modern computations
Matrices and their decompositions are the key
The tools are different for small-scale and large-scale problems
The idea is to give the basis for other IT courses in Comp. math. track
Python ecosystem will be used in a consistent manner for lectures and homeworks

Learning outcomes

Solve medium-scale numerical linear algebra problems (solve linear systems, compute eigenvalues and eigenvectors) 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)
Programming part of the homework will be distributed in the form of IPython notebooks



In [1]:

    
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0, 30, 128)
plt.plot(x, np.sin(2 * x))









    Out[1]:





[<matplotlib.lines.Line2D at 0x10e28c710>]

Syllabus

Week 1: Python crash course + some games with matrices
Week 2: Matrices, vectors, norms, ranks
Week 3: Linear systems, eigenvectors, eigenvalues
Week 4: Matrix decompositions (LU, QR, SVD) + test
Week 5: Sparse matrices and structured matrices
Week 6: Iterative methods / preconditioners / matrix functions
Week 7: Ping-pong + written test
Week 8: Application period

Homework

6 problem sets
Each friday (starting from the week 2) will be the deadline
Everybody has a resource of 5 days to postpone problem sets deadlines

Tests

2 written tests (week 4 and week 7)
Ping-pong test (week 7)

Books

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

Maxim Rakhuba: m.rakhuba@skolkovotech.ru
Ivan Oseledets: i.oseledets@skolkovotech.ru

Now let us go to Python intro



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]:



In [ ]: