It is a familiar fact that scientific software tends to do a lot of vector arithmetic and similar, that one does not want to keep rewriting the low-level code for such, so the usual practice is to use an off-the-shelf arithmetic library such as LINPACK.

I've been trying to track down the early history of such, and apparently the first such library was IBM's Scientific Subroutine Package (SSP), which was presumably bundled with IBM hardware in the early days (because IBM software in general was, prior to the great unbundling of 1969) and which seems to have been important and widely used in its day, until superseded by EISPACK in the early seventies.

An excellent, detailed account of the creation of EISPACK can be found at https://web.archive.org/web/20170702065825/http://history.siam.org/pdfs2/Dongarra_%20returned_SIAM_copy.pdf

Now, I'm trying to understand this history from the perspective of the people who were there at the time, and I keep trying to think of what I would do if I were a software manager at IBM, and it seems to me that I would consider it important to keep SSP up to date, keep it the number one choice, because that is something that could very well influence the purchase of computer equipment at academic institutions, which could later influence the purchase of equipment in business by students graduated from those academic institutions.

Was IBM's lunch simply eaten by a hungry and determined competitor? It doesn't quite look like that. From the above document, it seems that EISPACK was written by academics; in general, academics do not regard the writing of code is a high-value activity, but as something best avoided if reasonably possible; this does seem to have been the case here; from the above document:

That kind of software is always one of these funny things in terms of providing research funds. If you’re writing software, many people ask the question “where’s the research contribution in working on software, how does it affect us and why should we be paying for this?” So that’s been a constant source of problems from the political side in funding mathematical software on a level with some of the research that’s done in other areas. And sometimes we’d have to hide the fact that we’re writing software, so we’d say that we’re developing portable techniques...

It does, on reflection, feel a little surprising for the world's strongest IT company to be outcompeted by people who weren't even supposed to be spending their time writing code.

So what happened?

Did someone at IBM fall asleep at the wheel?

Did the EISPACK developers discover some new techniques so important that it was worth redoing a lot of programming work that had previously been done by a corporate team?

Did the EISPACK developers decide that portability was so important that it was worth redoing that work? If so, are there any statements on record from any of them explaining this decision and the reasoning behind it? The above document contains no indication of such.

Is there some other factor that I am missing?

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    I get the impression SSP was not nearly as extensive from reading a version of the 1130 Scientific Subroutine Package Programmer's Manual. (ibm1130.org/lib/manuals) – Brian Apr 11 at 11:35
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    In the 1960s IBM was losing its competitive position in high-end scientific computing. In fact an IBM internal memo forecast that by 1972 they would have lost 84% of that sector to competitors and they saw the biggest threat as the CDC STAR 100 vector processor (there was no mention of Cray Research in their forecasts!) The IBM 3090 "vector facility" only appeared in 1985, 11 years after the STAR 100 and 9 years after the Cray 1. Bascially, IBM were playing catch-up, not leading the field. – alephzero Apr 11 at 12:45
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    IBM later came back with its "Extended Scientific Subroutine Library", which included optimized implementations of BLAS and LAPACK – Brian Borchers Apr 12 at 3:21
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    @alephzero I thought Cray Research didn't even exist before 1972? Wasn't Seymour Cray still at Control Data Corporation (CDC) at the time that memo was written? – AJM-Reinstate-Monica Apr 12 at 11:49
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    IBM's primary business was selling hardware. Its software was targeted toward encouraging hardware sales. If they didn't have to develop the software, that was a win for them. SSP was pretty crude, so when better things came along, it was no longer needed. – John Doty Apr 12 at 16:39

Specifically concerning EISPACK. what happened was that James Hardy "Jim" Wilkinson in the UK (whose career as an applied mathematician started with practical ballistic modelling in WWII, working with Turing and other computing pioneers, and continued for the rest of his life at the UK National Physical Laboratory, not in some academic ivory tower) re-invented the entire foundation of computational linear algebra - or more accurately, gave it a practical foundation for the first time in the history of mathematics, with the new concept of "inverse" or "backward" error analysis.

Wilkinson's 700-page book from the 1960s "The Algebraic Eigenvalue Problem" is still a classic. The IBM SSP borrowed a couple of simple algorithms from it (plus another one invented by Jacobi way back in 1840s!) but EISPACK was "the whole nine yards." The EISPACK library only contained algorithms for eigenvalue problems. It had about 70 different algorithms, compared with four in IBM SSP.

EISPACK was not "written by academics" but created at Argonne National Lab in the USA, with the objective of being portable and free public domain software (And having cut his teeth working on EISPACK and LINPACK as a new graduate, Dongarra then went on to develop the LAPACK library which made both of them obsolete)

As an ironic footnote, Wilkinson was completely dismissive of a class of eigenvalue extraction methods now known as Arnoldi iteration, claiming (rightly) that they were of huge theoretical importance but (wrongly) could never be made to work in practical numerical analysis because of problems with rounding errors. Solutions to the numerical problems were discovered in the 1980s and these algorithms are now the "goto" standard methods for solving eigenproblems that are orders of magnitude bigger than anything Wilkinson could have imagined.

THE IBM SSP was also not competitive with commercial libraries such as IMSL (first released in 1970) which were much more comprenhensive (thousands of routines, not about 100) and not restricted to one computer manufacturer's products.

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    "Inverse error analysis" simple to understand, once it has been invented. If you solve a set of equations like Ax = b, the "obvious" question is "what is the difference between the calculated x and the exact solution?" Unfortunately, that question doesn't have a useful answer. Inverse error analysis asks "Suppose we have found the exact solution to the wrong problem. How close is the wrong problem to the one we wanted to solve - i.e. how much would we need to change A and/or b to make our calculated solution exact?" If A and b are measured data, that is a useful and practical question.. – alephzero Apr 11 at 13:07

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