On 22 Jul, 04:28, arithmonic <djes...@gmail.com> wrote: > On 21 jul, 17:39, "sttscitr...@tesco.net" <sttscitr...@tesco.net> > wrote: > > > On 21 Jul, 21:38, arithmonic <djes...@gmail.com> wrote: > > > > On 16 jul, 04:39, "sttscitr...@tesco.net" <sttscitr...@tesco.net> > > 1.- I challenge you to show such Eshbach's method in this thread, > because both of you are trying to state that my methods --based on the > Rational Mean-- are the same as the one you read in Eshbach's > work ("Handbook of Engineering Fundamentals).
I'm sure the poster knows what he read.
> 2.- I challenged you in this posting to show to the sci.math audience > a very simple numerical example on your alleged GENERAL Hurwitz's > ROOT-SOLVING METHOD for computing, say, THE FIFHT ROOT OF 2. There are 5 fifth roots of 2. Which one do you want ? Are you saying you can find complex roots too ?
Finding the real root of x^5-2 =0 is simple. s(x,y) is the sign of binary quntic x^5-2y^5
The root must lie between (0,1) = 0 and (1,0) = "inf" calculate s(0,1) and s(1,0). Form the mediant (1,1) At any stage in the process s(xn,yn) will be 1 or -1. if s(xn,yn) = un The new new mediant is formed with (xk,yk) where k is the largest index <n such that un*uk = -1