Cache-Friendly Low-Memory Lanczos in Rust

The efficient computation of eigenvalues and eigenvectors is a cornerstone in various scientific and engineering domains, including quantum mechanics, principal component analysis (PCA) in machine learning, structural mechanics, and network analysis. For large, sparse matrices, direct methods become computationally prohibitive, making iterative algorithms indispensable. The Lanczos algorithm stands out as a powerful iterative method for finding a few dominant eigenvalues and their corresponding eigenvectors of symmetric matrices. However, its effectiveness on modern hardware is often limited by two critical factors: memory consumption and cache performance. This article unpacks the key concepts behind implementing a cache-friendly, low-memory Lanczos algorithm in Rust, exploring how Rust’s unique features enable high-performance numerical computing.