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Stufe „Mittel“

Basic command of college-level mathematics (linear algebra and calculus). Basic level of programming proficiency: python programming language.

Ca. 18 Stunden zum Abschließen
Englisch
Untertitel: Englisch
Zertifikat zur Vorlage
Erhalten Sie nach Abschluss ein Zertifikat
100 % online
Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Flexible Fristen
Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.
Stufe „Mittel“

Basic command of college-level mathematics (linear algebra and calculus). Basic level of programming proficiency: python programming language.

Ca. 18 Stunden zum Abschließen
Englisch
Untertitel: Englisch

von

National Research University Higher School of Economics-Logo

National Research University Higher School of Economics

Lehrplan - Was Sie in diesem Kurs lernen werden

Woche
1

Woche 1

4 Stunden zum Abschließen

Machine arithmetics. Systems of linear algebraic equations.

4 Stunden zum Abschließen
11 Videos (Gesamt 61 min), 3 Lektüren, 2 Quiz
11 Videos
Introduction.56
A simple worked example.5m
Machine arithmetics. Representation of real numbers.6m
Machine epsilon. Over- and underflow.8m
A crude estimate of the machine epsilon.2m
Systems of linear equations. Cramer's rule.5m
Gaussian elimination.10m
LU decomposition: the matrix form of the Gaussian elimination.9m
When does the Gaussian elimination work?2m
LU decomposition with pivoting. Permutation matrices.8m
3 Lektüren
About the University10m
About the course10m
Slides10m
Woche
2

Woche 2

3 Stunden zum Abschließen

Numerical linear algebra.

3 Stunden zum Abschließen
12 Videos (Gesamt 72 min), 2 Lektüren, 1 Quiz
12 Videos
Sensitivity of a linear system.3m
Vector norms.5m
Matrix norms.3m
Common matrix norms.4m
Sensitivity of a linear system. Condition number.11m
Cholesky decomposition.7m
Banded matrices. Thomas algorithm.3m
Shermann-Morrison formula.8m
QR decomposition.6m
Constructing the QR decomposition: Householder reflections.13m
Constructing the QR decomposition: Givens rotations3m
2 Lektüren
Slides10m
Slides10m
Woche
3

Woche 3

3 Stunden zum Abschließen

Non-linear algebraic equations.

3 Stunden zum Abschließen
11 Videos (Gesamt 71 min), 1 Lektüre, 1 Quiz
11 Videos
Localization of roots. Bisection.4m
Fixed-point iteration.4m
Aside: convergence rates and related technicalities.7m
Back to the fixed-point iteration.11m
Fine-tuning the fixed-point iteration.5m
Newton's iteration.16m
Multiple roots. Modified Newton's method.3m
Inverse quadratic interpolation.4m
Roots of polynomials.3m
Roots of polynomials: the companion matrix.3m
1 Lektüre
Slides10m
Woche
4

Woche 4

2 Stunden zum Abschließen

Iterative method for linear systems.

2 Stunden zum Abschließen
8 Videos (Gesamt 55 min), 1 Lektüre, 1 Quiz
8 Videos
Simple iteration for a linear system. Jacobi iteration.8m
Convergence criteria for simple iteration.4m
Seidel's iteration.9m
Successive over-relaxation.3m
Canonic form of two-step iterative methods for linear systems.10m
Variational approaches: minimum residual method.5m
Copy of Simple iteration for a linear system. Jacobi iteration.8m
1 Lektüre
Slides10m

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