The necessities in Numerical Methods
Calculus
[edit | edit source]Numerical Differentiation
[edit | edit source]- Background on Differentiation (pdf)
- Continuous Function Differentiation (pdf)
- Discrete Function Differentiation (pdf)
- Forward, Backward, Central Divided Difference
- High Accuracy Differentiation
- Richardson Extrapolation
- Unequal Spaced Data Differentiation
- Numerical Differentiation with Octave
Numerical Integration
[edit | edit source]- Trapezoidal Rule
- Simpson's 1/3 Rule
- Romberg Rule
- Gauss-Quadrature Rule
- Adaptive Quadrature
Roots of a Nonlinear Equation
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Optimization
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Matrix Algebra
[edit | edit source]Simultaneous Linear Equations
[edit | edit source]- A system of linear equations (pdf)
Gaussian Elimination
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LU Decomposition
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Cholesky Decomposition
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LDL Decomposition
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Gauss-Seidel method
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Adequacy of Solutions
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Eigenvalue and Singular Value
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QRD
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SVD
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Iterative methods
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Regression
[edit | edit source]Linear Regression
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Non-linear Regression
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Linear Least Squares
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Interpolation
[edit | edit source]Polynomial Interpolation
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Linear Splines
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Piecewise Interpolation
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Ordinary Differential Equation
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Partial Differential Equation
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FEM (Finite Element Method)
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Using Symbolic Package in Octave
[edit | edit source]- Visit http://octave.sourceforge.net/index.html
- Download symbolic-1.0.9.tar.gz
- In Ubuntu, using the Ubuntu Software Center, I installed GiNac and CLN related software and symbolic package for Octave. But it did not properly installed.
- After extracting files from symbolic-1.0.9.tar.gz, I followed the following steps.
./configure ./make ./make INSTALL_PATH=/usr/share/octave/packages/3.2/symbolic-1.0.9
- While doing this, I got an error message related to mkoctfile. So, I used the following command: sudo apt-get install ocatve3.2-headers. Then I was able to install the symbolic packages in the Ubuntu.
Read some tutorials about symbolic computation
[edit | edit source]- Symbolic Mathematics in Matlab/GNU Octave (http://faraday.elec.uow.edu.au/subjects/annual/ECTE313/Symbolic_Maths.pdf)
- Symbolic Computations (http://www.math.ohiou.edu/courses/math344/lecture7.pdf)
Using SymPy ( a Python library for symbolic mathematics)
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