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

  • 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.
./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

Using SymPy ( a Python library for symbolic mathematics) edit

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