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Research & Projects

Research and programming projects by Jibon Krishna Joy, in computational mathematics, numerical methods, and scientific computing.
Relative Frobenius error against rank for Gaussian rSVD, SRHT-rSVD and randQB_EI on a 13,514 by 13,514 kernel matrix, with the exact SVD as the lower bound

Randomized Low-Rank Approximation of Kernel Matrices

Three randomized low-rank approximation algorithms written from scratch in Python and compared with the exact SVD on synthetic and boundary integral kernel matrices. The SRHT sketch has fewer operations than the Gaussian one, but it was slower and used much more memory in my tests.

Stability region of the classical fourth-order Runge-Kutta method

Numerical Algorithms in Python

Python code for the numerical methods from my Numerical Analysis I and II courses, with a notebook example for every method.

Surface plot of the numerical solution of the Poisson equation on the unit square

Numerical Methods for BVPs and PDEs

The ten problems from my Numerical Methods for Differential Equations course, solved in Python. All of them have an exact solution, so every notebook reports the real error.