Thread Links Date Links
Thread Prev Thread Next Thread Index Date Prev Date Next Date Index

Re: Possible Spam: Re: re motion 50 (Just to you...)

Am 26.09.2013 15:15, schrieb Ralph Baker Kearfott:

Ulrich et al,

On 09/26/2013 05:21 AM, Ulrich Kulisch wrote:

If this email is not spam, click here to submit the signatures to
FortiGuard - AntiSpam Service.
<http://nospammer.net/SubmitSpam/submitspam.php?id=I3RKBzJ3XzxyVAJfeUl.%0AUA__&sig=e3g2y5lyCe5oIzFgaiVlc3l4NC12MTPUAFdFHFAKSgYODxpfFVhWGhxKVwUJRAgUCxF%0AXTRgfUBsFDFAeHkwGHRxWV0obDloQVVNEFhBJDB8eVVlJF0JGBg1OVAIeCAoXVBpdS1tWHhMaQkc%0AFHkQRGBYWVUBbUlwaG1dQAh4IDBYXEUBJBRxXEQpCRQlHVgkYHR0ZXx5eRFI*dx8BCXoMFUQrdXM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%0AqJWdxeXg0LHYxGxwcV0FWRQoSBg5WWU0CWR0fAVcfCQ!

5QShgYFlkeWRQEMQNWXQUZRg1xeXgwLHY%0AxM3RoIylsaiVncXlqtTitZubFyoI6d.XfMzXN6AUsdjE3dGgjMWxqJX1xeXg1LHYb.gw0FWYD6Gq%0A8ZtELmroUeYw_>


Bill,


.
.
.

But let us assume that the gravitational constant appears as a datum
in a computation perhaps in a matrix multiplication. If you need a
guaranteed answer you would read it into the computer as an interval
where the bounds differ perhaps in the fifth digit. So you have to
compute a dot product with this interval in one component. You would
compute the minima and the maxima of the products of the vector
components and finally you have to accumulate all the minima and all
the maxima. Let us assume that this accumulation requires computing
the sum

10²⁰⁰ + 23456 -10²⁰⁰. (1)

If your computer provides an EDP you get the correct answer 23456 and
if the EDP is supported by hardware you get it very fast.

If your computer does not provide an EDP the average user will
accumulate (1) in conventional floating-point arithmetic and he gets
the wrong answer 0.



However, you will get the nearest floating point number to the
correct result, e.g., you would get 23456 in an IEEE double
type, if you have a correctly rounded dot product. P-1788 has
already decided a correctly rounded dot product will be included.

Baker


Baker,
then take a sum of dot products ab +cd + ef for vectors a, b, c, d, e, f and assume that the single correctly rounded dot products produce the summands of (1). Then the sum again gives you 0.
My personal answer is: The simplest way producing a correctly rounded dot product is via an EDP. 

Ulrich




--
Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik
D-76128 Karlsruhe, Germany
Prof. Ulrich Kulisch

Telefon: +49 721 608-42680
Fax: +49 721 608-46679
E-Mail: ulrich.kulisch@xxxxxxx
www.kit.edu
www.math.kit.edu/ianm2/~kulisch/

KIT - Universität des Landes Baden-Württemberg
und nationales Großforschungszentrum in der
Helmholtz-Gesellschaft