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中級

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

完成時間大約為18 小時
英語(English)
字幕:英語(English)
可分享的證書
完成後獲得證書
100% 在線
立即開始,按照自己的計劃學習。
可靈活調整截止日期
根據您的日程表重置截止日期。
中級

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

完成時間大約為18 小時
英語(English)
字幕:英語(English)

提供方

国立高等经济大学 徽標

国立高等经济大学

教學大綱 - 您將從這門課程中學到什麼

1

1

完成時間為 4 小時

Machine arithmetics. Systems of linear algebraic equations.

完成時間為 4 小時
11 個視頻 (總計 61 分鐘), 3 個閱讀材料, 2 個測驗
11 個視頻
Introduction.56
A simple worked example.5分鐘
Machine arithmetics. Representation of real numbers.6分鐘
Machine epsilon. Over- and underflow.8分鐘
A crude estimate of the machine epsilon.2分鐘
Systems of linear equations. Cramer's rule.5分鐘
Gaussian elimination.10分鐘
LU decomposition: the matrix form of the Gaussian elimination.9分鐘
When does the Gaussian elimination work?2分鐘
LU decomposition with pivoting. Permutation matrices.8分鐘
3 個閱讀材料
About the University10分鐘
About the course10分鐘
Slides10分鐘
2

2

完成時間為 3 小時

Numerical linear algebra.

完成時間為 3 小時
12 個視頻 (總計 72 分鐘), 2 個閱讀材料, 1 個測驗
12 個視頻
Sensitivity of a linear system.3分鐘
Vector norms.5分鐘
Matrix norms.3分鐘
Common matrix norms.4分鐘
Sensitivity of a linear system. Condition number.11分鐘
Cholesky decomposition.7分鐘
Banded matrices. Thomas algorithm.3分鐘
Shermann-Morrison formula.8分鐘
QR decomposition.6分鐘
Constructing the QR decomposition: Householder reflections.13分鐘
Constructing the QR decomposition: Givens rotations3分鐘
2 個閱讀材料
Slides10分鐘
Slides10分鐘
3

3

完成時間為 3 小時

Non-linear algebraic equations.

完成時間為 3 小時
11 個視頻 (總計 71 分鐘), 1 個閱讀材料, 1 個測驗
11 個視頻
Localization of roots. Bisection.4分鐘
Fixed-point iteration.4分鐘
Aside: convergence rates and related technicalities.7分鐘
Back to the fixed-point iteration.11分鐘
Fine-tuning the fixed-point iteration.5分鐘
Newton's iteration.16分鐘
Multiple roots. Modified Newton's method.3分鐘
Inverse quadratic interpolation.4分鐘
Roots of polynomials.3分鐘
Roots of polynomials: the companion matrix.3分鐘
1 個閱讀材料
Slides10分鐘
4

4

完成時間為 2 小時

Iterative method for linear systems.

完成時間為 2 小時
8 個視頻 (總計 55 分鐘), 1 個閱讀材料, 1 個測驗
8 個視頻
Simple iteration for a linear system. Jacobi iteration.8分鐘
Convergence criteria for simple iteration.4分鐘
Seidel's iteration.9分鐘
Successive over-relaxation.3分鐘
Canonic form of two-step iterative methods for linear systems.10分鐘
Variational approaches: minimum residual method.5分鐘
Copy of Simple iteration for a linear system. Jacobi iteration.8分鐘
1 個閱讀材料
Slides10分鐘

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