Re: HP 35s Matrix MultiTool 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 5.3672816017e18
Calculating the same determinant exactly (in Maple, using rational numbers) and then evaluating the resulting fraction to the same number of digits, I get 5.3672988874e18
So the Matrix MultiTool's answer has a relative error of 3.2e6.
How does the 48 do on this?
Stefan
The 48G gets 5.36728432771E18, but beware, this result should not be compared to 5.36729988736E18 because the calculator can't be expected to get that result. See my posting:
http://www.hpmuseum.org/cgisys/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 5.36728432456E18. 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
