My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 17th, 2018, 04:59 PM   #1
Newbie
 
Joined: Oct 2013

Posts: 20
Thanks: 0

Sign changes in computing Quartic function

Ferrari method uses simpler cubic equation.
For complex coefficients:
$\displaystyle (0.75, 1.25)x^4 + (1, 0)x^3 + (-1.25, 0)x^2 + (1.5, -0.25)x + (1.75, -1)$
p=(-0.358131487889273, 0.891003460207612),
q=(0.203643395074293, -1.232139222471),
r=(0.16504232468481, -1.24136744052394)
cubic:
$\displaystyle (1, 0)z^3 + (0.716262975778547, -1.78200692041522)z^2 + (-1.32579830222339, 4.32727697225848 )z + (-1.47669643119404, -0.501834028936385)$
give me:
z0=(0.0735802447326096, 0.597239257630761)
z1=(0.814183883954958, -0.378413964503688 )
z2=(0.216950841028975, 0.190838972431456)
thus
u0=(-0.957554480251324, 0.784814249702993),
u1=(0.523652798193374, -1.1664921945659),
u2=(-0.670813287658593, -0.0279863206956172),
u3=(1.10471496971654, 0.409664265558529)
and
x0=(-1.04578977436897, 0.931873073232405),
x1=(0.435417504075727, -1.01943337103649),
x2=(-0.75904858177624, 0.119072502833795),
x3=(1.0164796755989, 0.556723089087941)

BUT
for $\displaystyle (1.25, 1.25)x^4 + (1.75, -2)x^3 + (0.75, 0)x^2 + (1.5, 0.75)x + (0, -1.75)$
p=(1.14, -0.4125),
q=(1.22425, 0.32625),
r=(-0.6591203125, -0.306625)
cubic $\displaystyle (1, 0)x^3 + (-2.28, 0.825)x^2 + (3.765925, 0.286)x + (1.392349, 0.798823125)$
z0=(0.285858156895703, 0.0619552424669605)
z1=(0.316519149892536, -0.576284935944994)
z2=(0.362094330796378, 0.739640982532143)

I must change z0 to -z0 (or z1 to -z1 or z2 to -z2) and
z0=(-0.285858156895703, -0.0619552424669605)
u0=(-0.964471637584617, -0.22531128905411),
u1=(0.24028297599186, -1.25397067601018),
u2=(0.331433337799545, 1.3778811609441),
u3=(0.392755323793212, 0.101400804120189)
x0=(-0.939471637584617, 0.14968871094589),
x1=(0.265282975991861, -0.878970676010176),
x2=(0.356433337799545, 1.7528811609441),
x3=(0.417755323793212, 0.476400804120189)

In near 50% I must change. How determine, if I must change SIGN or not?

Last edited by skipjack; March 17th, 2018 at 09:07 PM.
Borneq is offline  
 
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
computing, function, polynomial, quartic, sign



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
sign function taylor_1989_2012 Calculus 5 October 4th, 2016 03:17 AM
Computing the error function fysmat Applied Math 7 March 1st, 2014 08:17 AM
Inverse Trig Function Problem --- sign ambiguity Niko Bellic Trigonometry 1 May 29th, 2012 08:29 PM
Sign diagram of a function meian2012 Linear Algebra 1 September 11th, 2010 03:33 PM
proof of discontinuity of sign function dannyboycurtis Real Analysis 2 October 26th, 2009 09:54 PM





Copyright © 2019 My Math Forum. All rights reserved.