The necessities in Numerical Methods
Calculus edit
Numerical Differentiation edit
- 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
- Trapezoidal Rule
- Simpson's 1/3 Rule
- Romberg Rule
- Gauss-Quadrature Rule
- Adaptive Quadrature
Roots of a Nonlinear Equation edit
Optimization edit
Matrix Computation edit
Simultaneous Linear Equations edit
Gausian Elimination edit
Eigenvalue and Singular Value edit
QRD edit
SVD edit
Iterative methods edit
Regression edit
Linear Regression edit
Non-linear Regression edit
Linear Least Squares edit
Interpolation edit
Polynomial Interpolation edit
Linear Splines edit
Piecewise Interpolation edit
Ordinary Differential Equation edit
Partial Differential Equation edit
FEM (Finite Element Method) edit
Using Symbolic Package in Octave edit
- 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
- 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