15c challenge: accuracy of a complex equation system

[John Keith]

(08-11-2023 07:56 AM)J-F Garnier Wrote:  Solution on Free42 (rounded to 10 digits):
I1 =  1.995795134 e-4  ,  4.096399075 e-3
I2 = -1.448833616 e-3  , -3.563298308 e-2
I3 = -1.454083170 e-3  , -3.563276083 e-2
I4 =  5.344581171 e-5  , -2.259868251 e-6



...

Note: the Free42 reference solution is obtained by using exactly the same system matrix with 10 significant digits, by doing SCI 9 RND on the system matrix before solving it.

The rounding itself introduces inaccuracies, although I understand the reasoning behind it. Since the values in the example are exact, the system can be solved using exact rational arithmetic. In case anyone is interested, here are the exact results rounded to 10 digits.

Code:


 ( 1.995795141E-4  ,  4.096399085E-3)   
 (-1.448833619E-3  , -3.563298308E-2)   
 (-1.454083174E-3  , -3.563276083E-2)   
 ( 5.344581171E-5  , -2.259868256E-6)

The Free42 results seem to be off by no more than 10 ULP's, not significant for most real-world uses.