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@@ -10,55 +10,9 @@ A lightweight, from-scratch, object-oriented Python package implementing classic
- Lightweight, no dependencies.
- Consistent object-oriented API (.solve() etc).
---
## Tutorial Series
This package comes with a set of Jupyter notebooks designed as a structured tutorial series in **numerical methods**, both mathematically rigorous and hands-on with code.
### Core Tutorials
1. [Tutorial 1: Vectors and Matrices](tutorials/tutorial1_vectors.ipynb)
- Definitions of vectors and matrices.
- Vector operations: addition, scalar multiplication, dot product, norms.
- Matrix operations: addition, multiplication, transpose, inverse.
- Matrix and vector norms.
- Examples with `numethods.linalg`.
2. [Tutorial 2: Linear Systems of Equations](tutorials/tutorial2_linear_systems.ipynb)
- Gaussian elimination and Gauss–Jordan.
- LU decomposition.
- Cholesky decomposition.
- Iterative methods: Jacobi and Gauss-Seidel.
- Examples with `numethods.solvers`.
3. [Tutorial 3: Orthogonalization and QR Factorization](tutorials/tutorial3_orthogonalization.ipynb)
- Inner products and orthogonality.
- Gram–Schmidt process (classical and modified).
- Householder reflections.
- QR decomposition and applications.
- Examples with `numethods.orthogonal`.
4. [Tutorial 4: Root-Finding Methods](tutorials/tutorial4_root_finding.ipynb)
- Bisection method.
- Fixed-point iteration.
- Newton’s method.
- Secant method.
- Convergence analysis and error behavior.
- Trace outputs for iteration history.
- Examples with `numethods.roots`.
- [Polynomial Regression Demo](tutorials/polynomial_regression.ipynb)
- Step-by-step example of polynomial regression.
- Shows how to fit polynomials of different degrees to data.
- Visualizes fitted curves against the original data.
---
This package comes with a set of Jupyter notebooks designed as a structured tutorial series in **numerical methods**, both mathematically rigorous and hands-on with code. See [Tutorials](./tutorials/README.md).
## Features