It solves the standard eigenvalue problem ( ) and the generalized problem (
Routines are modular, allowing users to calculate all eigenvalues, only a subset within a range, only the eigenvectors, or both. The Systematic Approach: The "Driver" Philosophy Matrix Eigensystem Routines — EISPACK Guide
Reorganizing algorithms into "blocked" versions that are significantly faster on modern hardware. It solves the standard eigenvalue problem ( )
In the early 1970s, the world of scientific computing was fragmented. While the Handbook for Automatic Computation by Wilkinson and Reinsch provided high-quality Algol 60 procedures for matrix computations, there was no standardized, portable, and rigorously tested library for the more widely used Fortran language. While the Handbook for Automatic Computation by Wilkinson
One of EISPACK's greatest innovations was the introduction of . While the library contains dozens of low-level "building block" routines—such as TRED1 for Householder reduction or IMTQL1 for the implicit QL algorithm—the drivers (like RG for general real matrices or RS for real symmetric matrices) simplified the user experience. A single call to a driver would handle the necessary transformations, the eigenvalue extraction, and the back-transformations of eigenvectors. Numerical Stability and the QR Algorithm