Combining the capabilities of both EISPACK and LINPACK (for linear equations) into a single framework. Why EISPACK Still Matters
The library handles real and complex matrices, including specific optimizations for symmetric, asymmetric, tridiagonal, banded, and Hessenberg forms.
It solves the standard eigenvalue problem ( ) and the generalized problem (
Specifically Level 3 BLAS, which performs matrix-matrix operations to maximize data reuse in cache.
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
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.
At the heart of EISPACK lies the , a robust iterative process that decomposes a matrix to find its eigenvalues. EISPACK’s implementation of this algorithm—specifically the versions handling the transformation to Hessenberg or tridiagonal form—remains a textbook example of balancing accuracy with computational economy. By using orthogonal transformations (like Householder reflections), the library ensures that rounding errors do not grow catastrophically during the process. Legacy and the Transition to LAPACK
By the late 1980s, the architecture of computers had changed. The rise of cache memory and vector processors meant that the "point-to-point" memory access patterns of EISPACK were no longer optimal. This led to the development of (Linear Algebra Package). LAPACK superseded EISPACK by: