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]

  • 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 | edit source]

Using SymPy ( a Python library for symbolic mathematics)[edit | edit source]

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