The necessities in Numerical Methods

From Wikiversity
Jump to navigation Jump to search

Calculus

[edit | edit source]

Numerical Differentiation

[edit | edit source]
  • Background on Differentiation (pdf)
  • 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 Algebra

[edit | edit source]

Simultaneous Linear Equations

[edit | edit source]
  • A system of linear equations (pdf)



Gaussian Elimination

[edit | edit source]


LU Decomposition

[edit | edit source]


Cholesky Decomposition

[edit | edit source]


LDL Decomposition

[edit | edit source]


Gauss-Seidel method

[edit | edit source]


Adequacy of Solutions

[edit | edit source]


Eigenvalue and Singular Value

[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.
./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]

Using SymPy ( a Python library for symbolic mathematics)

[edit | edit source]




go to [ Electrical_&_Computer_Engineering_Studies ]