Numerical methods that work
by Forman S. Acton · first published 1970
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2015–2025first – last mentioned
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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.
on “Other useless school trivia: the quadratic formula” ↗…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…
on “Building the System/360 Mainframe Nearly Destroyed IBM” ↗…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.
on “Python 3.11 is faster than 3.8” ↗…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.
on “Boycott Numerical Recipes (2007)” ↗