It solves the standard eigenvalue problem ( ) and the generalized problem (
EISPACK was designed to be a "pathway" system. Users would select a specific path of subroutines based on the characteristics of their matrix and the specific data required:
The library handles real and complex matrices, including specific optimizations for symmetric, asymmetric, tridiagonal, banded, and Hessenberg forms. Matrix Eigensystem Routines — EISPACK Guide
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.
In response, the NATS project (National Activity to Test Software), involving Argonne National Laboratory and various universities, began translating and refining these algorithms. The result was , a milestone in software engineering that prioritized numerical stability, documentation, and systematic testing over simple execution speed. Scope and Mathematical Coverage It solves the standard eigenvalue problem ( )
This overview details the history, structure, and enduring legacy of the library, the definitive collection of Fortran subroutines for solving matrix eigenvalue problems. The Genesis of Numerical Reliability
Despite being technologically superseded, the EISPACK Guide remains a foundational text for numerical analysts. It established the standards for , including the use of "check-results" and rigorous error analysis. The logic embedded in its Fortran IV code continues to serve as the "gold standard" for verifying the correctness of new numerical libraries across all modern programming languages. While the Handbook for Automatic Computation by Wilkinson
Should we focus on the for calling these routines, or would you prefer a comparison of execution speeds between EISPACK and its successor, LAPACK?