|Public apology to Valentin Albillo|
Message #1 Posted by fhub on 13 Nov 2011, 2:52 p.m.
First to our differences about the Laguerre method:
I now have to agree that you were right, the Laguerre algorithm is indeed a very powerful method and definitely better than the Bairstow algorithm!
What changed my mind? Well, today I've slightly modified my WP34s Laguerre program, and suddenly I got an error message which I couldn't explain. Analyzing this problem I found that there was a misunderstanding between me and the WP34s about the absolute value of a complex number: I assumed that [cpx]ABS would of course return just a single real value, but the WP34s implementation returns a complex value with the ABS-value in X and 0 in Y!
Since you have to compare 2 ABS-values of complex numbers in the Laguerre method (to find the larger denominator), I simply used a x>=y? after having calculated both absolute values, and so in fact I compared the 2nd abs-value with 0 (instead of the 1st abs-value), and this caused the program to always use the wrong denominator and so the iteration was so bad.
After having now corrected this program step (x>=z? instead of x>=y? to comply with this unexpected behaviour of the WP34s [cpx]ABS function), my Laguerre program now is working excellent and - as you said - indeed better than the Bairstow program (in average it needs only 1/3 of the iterations).
So in short words: you were right with Laguerre and I was wrong (due to my misunderstanding of this [cpx]ABS function in WP34s)!
Now about the 'style' of our communication:
Usually I'm a very friendly person and never use 'bad' words, but I was really angry about your answers to my postings with those numerous "Nope, ... is your lack of relevant theoretical knowledge",
"Nope, ... it's your lack of understanding", etc. etc. ...
You really treated me as if I would have "no clue about anything" (in other words, like being an idiot), and this may explain my reaction that I also answered in a quite unfriendly way.
So - although it was not only my fault - I nevertheless apology for my unfriendly and harsh words!
I hope you accept my apology,