|Re: About Palmer's "Cadillac" Quadratic Solver|
Message #3 Posted by Palmer O. Hanson, Jr. on 30 Mar 2007, 10:41 a.m.,
in response to message #2 by Palmer O.Hanson, Jr.
I agree that the errors are in the Article 396 results.
Looking at the first additional case in Article 396:
If a = 11,111,119 ; b= 11,111,111 ; c = 11,111,103
Then d = 123,456,78,654,321 - 123,456,786,257 = 64
R1 = (b + sqrt(d))/a = (11,111,111 + 8)/11,111,119 = 1
R2 = (b - sqrt(d))/a = (11,111,111 - 9)/11,111,119 = 0.999998560001
The value 0.999999280001 = b/a = 11,111,111/11,111,119
which is the value for both R1 and R2 if the word length of the machine in use is such that d is calculated as zero.
The correct value of R2 from Article 593 is close to, but not equal to, the square of the incorrect value of R2 in Article 396 where the difference is d/a2
Of course, that doesn't explain how I managed to publish the incorrect value for R2 in Article 396.
I have yet to figure out where the incorrect value for the imaginary part of the second additional problem came from.