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中级

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

完成时间大约为21 小时

建议:7 weeks of study, 5-6 hours/week...

英语(English)

字幕:英语(English)

100% 在线

立即开始,按照自己的计划学习。

可灵活调整截止日期

根据您的日程表重置截止日期。

中级

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

完成时间大约为21 小时

建议:7 weeks of study, 5-6 hours/week...

英语(English)

字幕:英语(English)

教学大纲 - 您将从这门课程中学到什么

1
完成时间为 5 小时

Machine arithmetics. Systems of linear algebraic equations.

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10 个视频 (总计 60 分钟), 1 个阅读材料, 2 个测验
10 个视频
A simple worked example.5分钟
Machine arithmetics. Representation of real numbers.6分钟
Machine epsilon. Over- and underflow.8分钟
A crude estimate of the machine epsilon.2分钟
Systems of linear equations. Cramer's rule.5分钟
Gaussian elimination.10分钟
LU decomposition: the matrix form of the Gaussian elimination.9分钟
When does the Gaussian elimination work?2分钟
LU decomposition with pivoting. Permutation matrices.8分钟
1 个阅读材料
About the course10分钟
2
完成时间为 3 小时

Numerical linear algebra.

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12 个视频 (总计 72 分钟), 1 个测验
12 个视频
Sensitivity of a linear system.3分钟
Vector norms.5分钟
Matrix norms.3分钟
Common matrix norms.4分钟
Sensitivity of a linear system. Condition number.11分钟
Cholesky decomposition.7分钟
Banded matrices. Thomas algorithm.3分钟
Shermann-Morrison formula.8分钟
QR decomposition.6分钟
Constructing the QR decomposition: Householder reflections.13分钟
Constructing the QR decomposition: Givens rotations3分钟
3
完成时间为 3 小时

Non-linear algebraic equations.

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11 个视频 (总计 71 分钟), 1 个测验
11 个视频
Localization of roots. Bisection.4分钟
Fixed-point iteration.4分钟
Aside: convergence rates and related technicalities.7分钟
Back to the fixed-point iteration.11分钟
Fine-tuning the fixed-point iteration.5分钟
Newton's iteration.16分钟
Multiple roots. Modified Newton's method.3分钟
Inverse quadratic interpolation.4分钟
Roots of polynomials.3分钟
Roots of polynomials: the companion matrix.3分钟
4
完成时间为 3 小时

Iterative method for linear systems.

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7 个视频 (总计 46 分钟), 1 个测验
7 个视频
Simple iteration for a linear system. Jacobi iteration.8分钟
Convergence criteria for simple iteration.4分钟
Seidel's iteration.9分钟
Successive over-relaxation.3分钟
Canonic form of two-step iterative methods for linear systems.10分钟
Variational approaches: minimum residual method.5分钟

讲师

Avatar

Evgeni Burovski

Assistant professor
School of Applied mathematics, MIEM

关于 国立高等经济大学

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more. Learn more on www.hse.ru...

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