A collection of numerical analysis algorithms implemented in Python alongside PDFs that explain error analysis with visualization plots.
This repository contains implementations of fundamental numerical methods alongside theoretical documentation:
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Linear Algebra: Iterative solvers for
$Ax = b$ and spectral analysis for eigenvalues. - Root-Finding: One-dimensional nonlinear equation solvers.
- Documentation: A comprehensive LaTeX PDF detailing the mathematical theory, convergence criteria, and performance comparisons.
- Gauss-Seidel Method: Iterative solver for systems of linear equations using the most recent updates at each step.
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Successive Over-Relaxation (SOR): Accelerated variant of Gauss-Seidel using a relaxation factor (
$\omega$ ) to speed up convergence. - Power Method: Iterative technique used to estimate the dominant eigenvalue and corresponding eigenvector of a matrix.
- Inverse Power Method: Variant used to find the smallest eigenvalue (or the eigenvalue closest to a target shift) using matrix inversion/decomposition.
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Fixed-Point Iteration: Solves
$x = g(x)$ by repeatedly evaluating the iteration function. -
Newton's Method: Rapidly converging root-finding technique utilizing function derivatives (
$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$ ).