A lightweight, from-scratch, object-oriented Python package implementing classic numerical methods.
No NumPy / SciPy solvers used, algorithms are implemented transparently for learning and research.

Why this might be useful

Great for teaching/learning numerical methods step by step.
Good reference for people writing their own solvers in C/Fortran/Julia.
Lightweight, no dependencies.
Consistent object-oriented API (.solve() etc).

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

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

Numerical Differentiation

Forward difference: ForwardDiff
Backward difference: BackwardDiff
Central difference (2nd order): CentralDiff
Central difference (4th order): CentralDiff4th
Second derivative: SecondDerivative
Richardson extrapolation: RichardsonExtrap

Matrix & Vector utilities

Minimal Matrix / Vector classes
@ operator for matrix multiplication
* for scalar-matrix multiplication
.T for transpose
Forward / backward substitution helpers
Norms, dot products, row/column access

Install (editable)

pip install -e /numethods

or just add /numethods to PYTHONPATH.

Examples

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|).