Sketch 'n Solve: An Efficient Python Package for Large-Scale Least Squares Using Randomized Numerical Linear Algebra

TL;DR

Sketch 'n Solve is a Python package that leverages randomized linear algebra techniques to efficiently solve large-scale least squares problems, significantly speeding up computations while maintaining accuracy.

Contribution

It provides a robust, user-friendly implementation of RandNLA methods for least squares, filling a gap in practical tools for large-scale problems.

Findings

Achieves up to 50x speedup over LSQR

Maintains high accuracy on ill-conditioned matrices

Effective for machine learning, signal processing, scientific computing

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.