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README.md

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 # numethods
 
+A small, from-scratch, object-oriented Python package implementing classic numerical methods.  
+**No NumPy / SciPy solvers used** — algorithms are implemented transparently for learning and research.
+
+## Features
+
+### Linear system solvers
+
+- **LU decomposition** (with partial pivoting): `LUDecomposition`
+- **Gauss–Jordan** elimination: `GaussJordan`
+- **Jacobi** iterative method: `Jacobi`
+- **Gauss–Seidel** iterative method: `GaussSeidel`
+- **Cholesky** factorization (SPD): `Cholesky`
+
+### Root-finding
+
+- **Bisection**: `Bisection`
+- **Fixed-Point Iteration**: `FixedPoint`
+- **Secant**: `Secant`
+- **Newton’s method** (for roots): `NewtonRoot`
+
+### Interpolation
+
+- **Newton** (divided differences): `NewtonInterpolation`
+- **Lagrange** polynomials: `LagrangeInterpolation`
+
+### Orthogonalization, QR, and Least Squares (NEW)
+
+- **Classical Gram–Schmidt**: `QRGramSchmidt`
+- **Modified Gram–Schmidt**: `QRModifiedGramSchmidt`
+- **Householder QR** (numerically stable): `QRHouseholder`
+- **QR-based linear solver** (square systems): `QRSolver`
+- **Least Squares** for overdetermined systems (via QR): `LeastSquaresSolver`
+
+### Matrix & Vector utilities
+
+- Minimal `Matrix` / `Vector` classes
+- `@` operator for **matrix multiplication** (NEW)
+- `*` for **scalar**–matrix multiplication
+- `.T` for transpose
+- Forward / backward substitution helpers
+
+---
+
+## Install (editable)
+
+```bash
+pip install -e /numethods
+```
+
+or just add `/numethods` to `PYTHONPATH`.
+
+## Examples
+
+```bash
+python /numethods/examples/demo.py
+```
+
+## Notes
+
+- All algorithms are implemented without relying on external linear algebra solvers.
+- Uses plain Python floats and list-of-lists for matrices/vectors.
+- Tolerances use a relative criterion `|Δ| ≤ tol (1 + |value|)`.

pyproject.toml

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+[build-system]
+requires = ["setuptools>=61.0"]
+build-backend = "setuptools.build_meta"
+
+[project]
+name = "numethods"
+version = "0.1.0"
+description = "Some numerical methods implemented in Python"
+authors = [
+    { name = "Deniz Donmez", email = "denzdonmez@gmail.com" }
+]
+readme = "README.md"
+requires-python = ">=3.8"
+license = { text = "MIT" }
+
+[tool.setuptools.packages.find]
+where = ["."]
+include = ["numethods"]