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Nivel intermedio

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

Aprox. 18 horas para completar
Inglés (English)

Instructor

Certificado para compartir
Obtén un certificado al finalizar
100 % en línea
Comienza de inmediato y aprende a tu propio ritmo.
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Nivel intermedio

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

Aprox. 18 horas para completar
Inglés (English)

ofrecido por

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National Research University Higher School of Economics

Programa - Qué aprenderás en este curso

Semana
1

Semana 1

4 horas para completar

Machine arithmetics. Systems of linear algebraic equations.

4 horas para completar
11 videos (Total 61 minutos), 3 lecturas, 2 cuestionarios
11 videos
Introduction.56s
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 lecturas
About the University10m
About the course10m
Slides10m
Semana
2

Semana 2

3 horas para completar

Numerical linear algebra.

3 horas para completar
12 videos (Total 72 minutos), 2 lecturas, 1 cuestionario
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 lecturas
Slides10m
Slides10m
Semana
3

Semana 3

3 horas para completar

Non-linear algebraic equations.

3 horas para completar
11 videos (Total 71 minutos), 1 lectura, 1 cuestionario
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 lectura
Slides10m
Semana
4

Semana 4

2 horas para completar

Iterative method for linear systems.

2 horas para completar
8 videos (Total 55 minutos), 1 lectura, 1 cuestionario
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 lectura
Slides10m

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