According to the WordPress statistics, this blog received over 42,000 visitors and 73,000 views in 2018. These are the ten most-viewed posts published during the year.

- How to Program log z
- Tricks and Tips in Numerical Computing
- Conversations with Gil Strang
- What’s New in MATLAB R2018a?
- Numerical Linear Algebra Group 2017
- Bohemian Matrices in Manchester
- Half Precision Arithmetic: fp16 Versus bfloat16
- Palomino Blackwing Pencil Tribute to Ada Lovelace
- Joan E. Walsh (1932–2017)
- Lectures on Multiprecision Algorithms in Kácov

In addition, the article Differentiation With(out) a Difference in my SIAM News “From the SIAM President” column was the most viewed SIAM News article of 2018.

Recently I tried using the complex step derivative with stepsize taken to be the denorm min. It resulted in catastrophic inaccuracy. Yet I cannot find anything in the reasoning you present that would cause this. So I tried running some simulations and found that the highest accuracy occurred when taking the step as twice the unit roundoff, which was very surprising since I thought the min would be most accurate.

I feel like there is more to understand about the complex step derivative than we currently know.

If by “denorm min” you mean smallest normalized number or even smallest subnormal number then I think what you’re seeing is not surprising. I would want to stay well away from the subnormal numbers, as they have less precision than normalized numbers. Some analysis of your problem certainly seems warranted.