The necessities in Numerical Methods

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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.
./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


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




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