Re: back to the roots

["G. William (Bill) Walster" <bill@xxxxxxxxxxx>]

Ulrich,

Are you not assuming that your original linear system to which you got an approximate solution is infinitely precise?

Otherwise what do you mean by: "It may be difficult to understand that an "approximate" solution of which possibly no digit is correct all of a sudden is assumed being infinitely precise. But that's the way it is. All this has nothing to do with measured data."

What do you mean by "no digit [in the approximate solution] is correct"?  Do you mean that the approximate solution is not contained in the interval solution to the original non-degenerate interval linear system?

It seems to me that the above quotation only makes sense if the original linear system is infinitely precise.

Cheers,

Bill


On 7/1/13 12:47 AM, Ulrich Kulisch wrote:

Am 28.06.2013 19:07, schrieb Bill:

Ulrich,

Can you cite one practical real world example of a computation, other than one in pure mathematics, in which all inputs are infinitely precise degenerate intervals?  That might help to motivate your perceived desire for a long accumulator.

My answer was this:

<Assume you somehow got an approximate solution of a linear system and you want to improve it by a defect <correction. Then you assume of course that the data of the approximate solution are infinitely precise. Even if <no digit of the "approximate" solution is correct you can with Rump's method compute a highly accurate <enclosure. Also here you assume that the "approximate" solution is infinitely precise.

It may be difficult to understand that an "approximate" solution of which possibly no digit is correct all of a sudden is assumed being infinitely precise. But that's the way it is. All this has nothing to do with measured data.

Best regards
Ulrich

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