numerical-calculus-octave-scripts
Octave/Matlab functions and scripts related to "Calcolo Numerico e Laboratorio" course in UNIFE (University of Ferrara), year 2015-2016.
What this repository is about
This repository is a collection of Octave/Matlab scripts and functions which you can freely use.
To be able to run these scripts with Matlab you may need to change some instructions. These scripts, infact, have only been tested with GNU Octave, a free (as in freedom) version of Matlab. If you use Matlab you should switch to Octave instead and maybe even contribute to that project.
Before writing these scripts and functions, there is (usually) a certain amount of paper work to be done (i.e. getting paper and pen and, while reading codes or theory, think and write about what, why and how it's done). This means that to fully understand what is going on you should spend some time on it, unless you are very good at maths :) and can grasp all the concepts at first glance.
Fell free to contribute to this repository.
Covered arguments
- General Octave/Matlab training.
- Miscellaneous
- Horner's method to evaluate polynomials.
- Error evaluations.
- Relative and absolute errors.
- Condition number of square matrices.
- Number conversions
- Integers from base b1=10 to base b2.
- Floating between 0 and 1 from b1=10 to b2.
- From base b1 to base b2=10.
- From base b1 to base b2 (it covers all the previous cases).
- Linear systems solving
- Diagonal matrices.
- Lower matrices.
- Upper matrices.
- Matrix factorization
- A = LR
- PA = LR
- Standard case.
- Non square matrices.
- Band matrices with bandwidth r.
- Tridiagonal matrices using Thomas's algorithm.
- PAQ = LR
- A = QR (with Givens rotations)
- Standard case.
- Hessenberg matrices.
- A = RQ (with Givens rotations)
- Iterative methods
- Iacobi.
- Gauss Seidel.
- Parametrized Iacobi.
- SOR.
- Interpolation
- Interpolation using Vandermonde matrix.
- Lagrange polynomial.
- Chebyshev polynomial
- Trigonometric formula.
- Iterative formula.
- Chebyshev nodes.
- Divided differences
- For Newton's polynomial.
- For Hermite's polynomial.
- Newton polynomial
- Standard interpolation.
- Piecewise interpolation.
- Hermite polynomial
- Standard interpolation.
- Piecewise cubic interpolation.
- Splines
- Linear splines.
- Cubic splines.
- Approximation
- Linear regression
- Generic.
- Polynomial.
- Linear regression
- Non-linear equations
- Bisection method.
- Fixed point method.
- Newton's method.
Function file structure
License notice
Function prototype
Function prototype (printable)
Brief description of what the function does
[Explanation of mathematical theory]
I: Input[s]
P: Propriety[es] of input P
O: Output[s]
C: Consequence[s]
Function code
License
Every file in this repository is covered by the WTFPL. We decided not to use the GPL because all these are implemetations of well known mathematical cases, so the copyleft clause and others clauses are not necessary here.