numethods/tutorials/README.md

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

   • 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

   • 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

   • 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

   • 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

• Step-by-step example of polynomial regression.

• Shows how to fit polynomials of different degrees to data.

• Visualizes fitted curves against the original data.

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