Sketch 'n Solve: An Efficient Python Package for Large-Scale Least Squares Using Randomized Numerical Linear Algebra
Abstract
We present Sketch 'n Solve, an open-source Python package that implements efficient randomized numerical linear algebra (RandNLA) techniques for solving large-scale least squares problems. While sketch-and-solve algorithms have demonstrated theoretical promise, their practical adoption has been limited by the lack of robust, user-friendly implementations. Our package addresses this gap by providing an optimized implementation built on NumPy and SciPy, featuring both dense and sparse sketching operators with a clean API. Through extensive benchmarking, we demonstrate that our implementation achieves up to 50x speedup over traditional LSQR while maintaining high accuracy, even for ill-conditioned matrices. The package shows particular promise for applications in machine learning optimization, signal processing, and scientific computing.
Cite
@article{arxiv.2409.14309,
title = {Sketch 'n Solve: An Efficient Python Package for Large-Scale Least Squares Using Randomized Numerical Linear Algebra},
author = {Alex Lavaee},
journal= {arXiv preprint arXiv:2409.14309},
year = {2024}
}