Skip to content

Continued fractions!!

Upon reading this note by John Cook on continued fractions, I wrote:

If you like continued fractions, I recommend you read the relevant parts of the classic Numerical Methods That Work. The details are probably obsolete but it’s fun reading (at least, if you think that sort of thing is fun to read).

I then looked up Acton in Wikipedia and was surprised to see he’s still alive. And he wrote a second book (published at the age of 77!). I wonder if it’s any good. It’s sobering to read Numerical Methods That Work: it’s so wonderful and so readable, yet in this modern era there’s really not much reason to read it. Perhaps William Goldman (hey, I checked: he’s still alive too!) or some equivalent could prepare a 50-page “good parts” version that could be still be useful as a basic textbook.


  1. old fogey says:

    You wrote: “yet in this modern era there’s really not much reason to read it.”

    I don’t quite follow that assertion. Is the point that libraries are so sound now that an analyst can trust them? My own view is that numerical problems can sneak on on users and that they need to be educated to be paranoid regarding the results of floating point computations. But, maybe I am old fashioned.

    Доверя́й, но проверя́й.

  2. Ken Butler says:

    I love “Numerical Methods That Work”. You don’t see books written like that any more.

    Whether it’s worth reading or not depends on where you’re coming from, I guess. As something that students (of computer science especially) should know, I think it’s still very important, but as a practitioner using this stuff nowadays, maybe not so much.

    (I’m a statistician, but I learned some of this stuff years ago, and I’m glad I did.)

    • old fogey says:

      Well, actually among the rather strange set of activities that make up my professional life, I am a part-time professor of computer science. So, perhaps that explains my views.

      But, my general approach is that it is a good idea to get any numerical answer, especially for non-discrete problems, by two different calculations. Not different implementations of the same calculation but different approaches to the calculation. This is for one-off analyses. Obviously, for a repeated calculation, say a GPS receiver, build a single, carefully debugged and tested, computational package.

      still a fogey

    • Rahul says:

      The “efficiency” part of that book has become somewhat irrelevant to 90% of computer users since it has become so much cheaper to throw raw computing power at the problem.

      How many of us deal with problems where computation time is really the limiting factor?

      • Maybe you don’t but in engineering and physical sciences we do all the time. Here’s an example: create a bayesian posterior for the wave velocity structure of the earth’s crust in a region with your only data being a series of seismometer waveforms at a small fixed number of stations. If you want to do MCMC based methods you’ll have to solve the full elastodynamics of the crust for each event at every proposal.

  3. […] Gelman, Statistical Modeling, Causal Inference, and Social Science, Continued Fractions, here. Quite a shout out to […]

  4. Bruce McCullough says:

    Let’s refer correctly to the title of Acton’s superb book. True, if you look it up in a card catalog, it’s “Numerical Methods that Work” but if you look at the cover of the hardback version, the word “usually” is embossed without color between “that” and “Work”. On the paperback version, the word “usually” is printed in a faint color.

    His other book, “Real Computing Made Real” is less technical and more chatty, but still a good read. Likens using Mathematica to JP Morgan’s comment about yachts: yes, Mathematica will solve your problem, but if you have to ask then you don’t know enough to use Mathematica to solve your problem.