Re: HP 35s Matrix Multi-Tool Message #13 Posted by Rodger Rosenbaum on 5 Nov 2007, 2:32 a.m., in response to message #11 by Stefan Vorkoetter
Quote:
Just tried a 6x6 Hilbert matrix. The program comes up with a determinant of 5.3672816017e-18
Calculating the same determinant exactly (in Maple, using rational numbers) and then evaluating the resulting fraction to the same number of digits, I get 5.3672988874e-18
So the Matrix Multi-Tool's answer has a relative error of 3.2e-6.
How does the 48 do on this?
Stefan
The 48G gets 5.36728432771E-18, but beware, this result should not be compared to 5.36729988736E-18 because the calculator can't be expected to get that result. See my posting:
http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv015.cgi?read=72273#72273
The correct value to use as the standard of comparison for a calculator that uses 12 digit numbers in its calculations is 5.36728432456E-18. Using this as a standard of comparison, the HP48G got 3 more correct digits than your 35S program. This is the expected result since the 48G uses 15 digit arithmetic for the calculation, 3 more than you're using.
The LCM of the denominators in a 6x6 Hilbert matrix, if you want to use the other method I mentioned in the earlier post, is 27720. The determinant in that case should be exactly 2435091120, but the HP48G gets 2435091119.56
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