Largest Eigenvalue Optimization

Overview

This skill provides guidance for optimizing numerical computations that need to outperform standard library implementations like numpy or scipy. The primary focus is on finding the largest eigenvalue of small dense matrices, but the principles apply broadly to numerical optimization tasks.

When to Use This Skill

• Optimizing eigenvalue computations to beat numpy.linalg.eig performance
• Performance-critical numerical linear algebra on small dense matrices (2x2 to ~100x100)
• Tasks requiring Cython extensions that call LAPACK directly
• Any numerical optimization where Python wrapper overhead is the bottleneck

Critical First Step: Profile Before Optimizing

Before attempting any optimization, understand where time is actually spent.

1. Profile the reference implementation to identify the bottleneck:
   • Is time spent in the algorithm itself (LAPACK routines)?