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[Paul Dale]

(01-29-2016 09:09 AM)ColinJDenman Wrote:  It would not be beyond wit or wisdom for a modern calculator to perform a similar analysis of error margin (due to calculation) and present the answer in similar form.

It is beyond large computers to do this automatically and it is what keeps numeric analysts employed. The reason is that any error bounds explode very quickly and give a useless range as a result. For example: 10±1 ⨉ 12±1 = 121±22. A small error in the last digits will be compounded quickly, more so for functions with steep gradients.

It is possible for algorithms to be designed so that they produce a narrower result but I'm not aware of anything automated that can do this reliably. An additional confounding factor is that, by design, a calculator is always working one step at a time and cannot have an holistic view of the computation.

A good book on the subject is Validated Numerics by Tucker.


- Pauli