From R. Baker Kearfott Dear Colleagues:

There has been some discussion recently about standardizing notation
for intervals within research and review papers and books. One
suggestion
has been to use the notation in my forthcoming Kluwer
monograph *Rigorous Global Search: Continuous Problems.* I'd
like to comment on this.

Basically, I have used boldface to denote intervals and usual math italic to denote point quantities. I have used underscores to denote lower bounds and overscores to denote upper bounds.

A device that has generated some controversy is my use of uppercase for both vectors and matrices. In particular, a more usual practice in numerical linear algebra is to reserve uppercase for matrices only, and to use lowercase for vectors; vectors are then distinguished from components by use of subscripts. I agree with this modification to my notation.

I am in general agreement that a standardized notation would be advantageous. However, before we force any particular notation (such as requiring a particular notation in submissions to Reliable Computing), we should probably have more discussion, as well as some mechanism for coming to a consensus. If there is a strong feeling for a standardized notation, I can organize this.

Best regards,

Baker

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