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)

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|).

1.7 KiB Raw Blame History Unescape Escape