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

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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|).