The necessities in Numerical Methods
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Calculus[edit | edit source]
Numerical Differentiation[edit | edit source]
- Continuous Function Differentiation
- Discrete Function Differentiation
- 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[edit | edit source]
Optimization[edit | edit source]
Matrix Computation[edit | edit source]
Simultaneous Linear Equations[edit | edit source]
Gausian Elimination[edit | edit source]
Eigenvalue and Singular Value[edit | edit source]
QRD[edit | edit source]
SVD[edit | edit source]
Iterative methods[edit | edit source]
Regression[edit | edit source]
Linear Regression[edit | edit source]
Non-linear Regression[edit | edit source]
Linear Least Squares[edit | edit source]
Interpolation[edit | edit source]
Polynomial Interpolation[edit | edit source]
Linear Splines[edit | edit source]
Piecewise Interpolation[edit | edit source]
Ordinary Differential Equation[edit | edit source]
Partial Differential Equation[edit | edit source]
FEM (Finite Element Method)[edit | edit source]
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)[edit | edit source]