# numerical-methods
### Repository with the purpose of helping the ones in need on their path to achieving the computer science numerical wisdom. Contains MATLAB/Octave (and Python/C++ soon) implementations of the algorithms.

### Implemented algorithms

#### Nonlinear Equations

| | Matlab | Python | C++ |
| --- | --- | --- | --- |
| Bisection method| :octocat: | | |
| Newton-Raphson method | :octocat: | | |
| Secant method | :octocat: | | |

#### Gaussian methods

| |Matlab|Python|C++|
|---|---|---|---|
|Gaussian elimination|:octocat:|||
|Gaussian elimination with Partial Pivoting|:octocat:|||
|Gaussian elimination with Scaled Partial Pivoting|:octocat:|||
|Gaussian elimination with Total Pivoting|:octocat:|||

#### LU Factorization methods

| |Matlab|Python|C++|
|---|---|---|---|
|Doolittle|:octocat:|||
|Crout|:octocat:|||
|Cholesky|:octocat:|||

#### QR Factorization methods

| |Matlab|Python|C++|
|---|---|---|---|
|Givens|:octocat:|||
|Gram-Schmidt|:octocat:|||
|Householder|:octocat:|||

#### Iterative methods

| |Matlab|Python|C++|
|---|---|---|---|
|Gauss-Seidel|:octocat:|||
|Jacobi|:octocat:|||
|Successive over-relaxation (SOR)|:octocat:|||

#### Eigenvalues decomposition

| |Matlab|Python|C++|
|---|---|---|---|
|Power method|:octocat:|||
|Inverse Power method|:octocat:|||
|Deflation method|:octocat:|||

#### Ad-hoc algorithms

| |Matlab|Python|C++|
|---|---|---|---|
|Diagonally dominance|:octocat:|||
|Positive definition|:octocat:|||
|Triangular matrices evaluation|:octocat:|||
|Gershgorin circles|:octocat:|||
|Gauss-Jordan Matrix Inverse|:octocat:|||

### Convention

- Before starting working on something, check the "Pull requests" tab to see if there isn't anyone who's already doing the same thing!
- Convention: The sources' names will start with a capital letter: "Crout", "Doolittle", "Householder", "Givens" etc.
- Comment your sources!
- Test your sources with several input cases: eye matrix, full matrix, triu matrix, tril matric, random matrix, small, big etc.
- Use notation tags:
	- [NOTE] for related notes
	- [USES] for sources which use other sources that are in a different folder to suggest that the user should first copy the dependencies (sources needed) in the same folder for testing 
- before creating a Pull Request, it should look like this: [Householder](https://github.com/radusqrt/help-the-kids/blob/master/MN/Algoritmi/QR/Householder/Householder.m)

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### Python coding style
https://github.com/google/yapf

### Contributors

This project exists thanks to all the people who <a href="https://github.com/radusqrt/numerical-methods/graphs/contributors">contribute</a>.

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Other repositories that might be of interest:
1. [Algorithm design repository](https://github.com/radusqrt/algorithm-design)
2. [Computer Programming repository](https://github.com/radusqrt/computer-programming)