Numerical methods that work

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1. PaulHouleApr 2025
   (1) Maybe I'm just a little too young but my impression was that the 360 and it's successors were not that big in scientific computing, certainly there were some big academic installations but I saw a lot more DEC machines (PDP-8 in the experimental lab, PDP-10, PDP-11 and VAX elsewhere) and by the time I went to college circa 1990 you were likely to see Motorola 68k-based "workstations" that were quickly replaced by RISC architectures like SPARC and PA-RISC which in turn failed to compete with the PC.

   Cornell had one of very few IBM 3090s with a vector unit (to compete with the Cray) just before I showed up, but when I did IBM had donated a message-passing based supercomputer based on the Power PC architecture. I only saw a 3090 (no vector unit) at New Hampshire Insurance which I got to use as a Computer Explorer.

   (2) I was taught in grad school in the 1990s to use floats if at all possible to reduce the memory requirements of scientific codes if not actually speed up the computation. (In the 1990s floats were twice as fast as doubles on most architectures but not the x86). I really enjoyed taking a course on numerics from Saul Teukolsky, what stood out in the class as opposed my reading to the Numerical Recipes book which he was a co-author of, was the part about the numerical stability of discretizing and integrating partial differential equations. If you did it wrong, unphysical artifacts of the discretization would wreck your calculation. Depending on how you did things rounding errors can be made better or worse, Foreman Action's Numerical Methods that Work and later Real Computing Made Real reveal techniques for managing these errors that let you accomplish a lot with floats and some would point out that going to doubles doesn't win you that much slack to do things wrong.

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2. itazulaMar 2015
   Solving it by hand gives an exact answer, which in some contexts, might be preferable. Forman Acton, in his classic book, Numerical Methods That Work, uses the quadratic formula as an example to illustrate how a computer can give a wildly incorrect solution.
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3. PaulHouleOct 2022
   Yep.

   FORTRAN codes persist today because (1) the old school memory model of FORTRAN is fast, and (2) it is so easy to write numeric codes that do the wrong thing with rounding and numerical instability. There's a reason why Foreman Acton wrote a book titled Numerical methods that (usually) work.

   https://www.amazon.com/Numerical-Methods-that-Work-Spectrum/...

   Code something up in C, Haskell, oCAML or CUDA and you miss out on the 40+ years of experience people have had with a FORTRAN code from the 1970s.

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4. gnufxApr 2022
   To support the sibling: If we're talking history, the assumption in the early 80s was that software was shared, at least in the technical computing circles I lived in and to the extent it was portable enough. We were suspicious of people who kept code under wraps -- with good reason in some cases that dubiously reproduced data post hoc, which was an early lesson. Free Software per se was a reaction to that culture being eroded around rms earlier than I saw it, and it's basically what I've done since I started.

   I'm not convinced about "black art" given, for instance, the Harwell library and later NAG, although they weren't free software. (I knew about Ian Grant's work as an undergraduate, though he didn't teach me.) Later I knew how to get code from Netlib by email before we had general trans-Atlantic network access.

   I found Nick Higham has a soft spot for the undergraduate textbook we had, from rather earlier, Acton's Numerical Methods that Work.

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