Numerical and Monte Carlo Algorithms Library

Abstract

This project is a series of experimental numerical-computing builds centered on algorithmic design, floating-point behavior, and convergence diagnostics. The work covers canonical methods from numerical analysis and Monte Carlo simulation, implemented as modular routines to support reproducibility and direct benchmarking.

The libraries include routines for dense matrix operations, matrix factorizations, interpolation and splines, linear and non-linear system solvers, and numerical quadrature. On the Monte Carlo side, the work includes non-uniform random variable generation, quasi-Monte Carlo quadrature, statistical diagnostics, and variance reduction techniques.

Across reports, theoretical predictions are validated with numerical experiments, including reproductions of standard results from the literature and visualized empirical outcomes.

Main contributions

• Implemented core numerical-analysis and Monte Carlo algorithms independently in MATLAB/Julia workflows (with earlier implementations in Python).
• Built reproducible, modular libraries suitable for side-by-side testing against reference methods.
• Benchmarked implementations against canonical results from the literature and documented comparative outcomes with detailed analysis reports.
• Analyzed numerical stability, convergence rates, and computational trade-offs across algorithm classes.
• Validated analytical/theoretical expectations through controlled simulation studies and report-based experiments.

Analysis Report Archives (PDF)

Conclusions

This project establishes a reusable foundation for classical scientific-computing workflows, from deterministic numerical methods to simulation-based estimation. The combined repositories and report archive emphasize implementation clarity, verification, and reproducibility, and they serve as a base for future extensions in high-performance and application-driven computational research.