[SystemSafety] Accuracy of COVID modeling code

[Olwen Morgan]

... and, a thousand apologies, I forgot to mention also the following text:

/Validated Numerics: A Short Introduction to Rigorous Computations/, 
Warwick Tucker, Princeton University Press, 25th July 2011, 
ISBN-10:0691147817, ISBN-13:978-0691147819


... Sorry for the absent-mindedness .... only just got my concentration 
back after a dire winter off the happy pills (for medical reasons) and 
struggling all the way with with SAD,



regards,

Olwen






On 22/05/2020 11:36, Olwen Morgan wrote:
>
>
> I agree that choice of algorithm is much more important than compiler 
> optimisations. Indeed, a reliance on compiler optimisations is often, 
> in my experience, a sign of underlying ignorance of relevant numerical 
> algorithms. This is particularly visible when, using an iterative 
> numerical method, one does not pay sufficient - or as is often the 
> case absolutely no - attention to getting good starting values. 
> Another mortal sin is to forget about strict error bounds. Chebyshev 
> always insisted on them and he was one of the founders of modern 
> approximation theory.
>
> And as regards summing numbers in ascending order of magnitude, yes, 
> it is better than summing them in no particular order, but there still 
> pitfalls for the unwary even when ascending order is used. The best 
> short text on this is, IMHO:
>
> /Rounding Errors in Algebraic Processes/, J. H. Wilkinson, Dover 
> Publications
>
> though it's hard to get hold of and can cost an arm and a leg even 
> when you can find it.
>
>
> regards,
>
> Olwen
>
>
> On 10/05/2020 15:54, Peter Bishop wrote:
>> Exact results are pretty unlikely for FP.
>> But on the other hand, I think the *numerical algorithm* is probably 
>> more important than any local HLL optimisations in reducing rounding 
>> errors,
>> e.g. when adding an array of FP numbers, the best option is to sort 
>> them an ascending order before sequentially adding them.
>>
>> Peter Bishop
>>
>> On 09/05/2020 18:21, Peter Bernard Ladkin wrote:
>>> On 2020-05-09 18:41 , Derek M Jones wrote:
>>>> Section 5.1.2.3 of the C Standard,
>>>>
>>>> or sentence 189:https://c0x.coding-guidelines.com/5.1.2.3.html
>>>> "In the abstract machine, all expressions are evaluated as specified by the semantics."
>>> Which should mean that the expression "x^2 - y^2" returns the square of the value of x minus the
>>> square of the value of y. What is called the exact value.
>>>
>>> What a poor piece of writing.
>>>
>>> PBL
>>>
>>> Prof. Peter Bernard Ladkin, Bielefeld, Germany
>>> Styelfy Bleibgsnd
>>> Tel+msg +49 (0)521 880 7319www.rvs-bi.de
>>>
>>>
>>>
>>>
>>>
>>>
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>> -- 
>>
>> Peter Bishop
>> Chief Scientist
>> Adelard LLP
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>>
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