Register to reply

Perturbed function

by sprinkle
Tags: function, perturbed
Share this thread:
sprinkle
#1
Nov20-09, 04:03 PM
P: 3
Consider the polynomial: f(x)= x^5- 300x^3- 126x+ 5005
which has a root alpha= 5. Also consider the perturbed function
F_e(x)= f(x)- epsilon x^5= (1- epsilon)x^5- 300x^3- 126x+ 5005
where epsilon is a small number. Letting alpha(epsilon) denote the perturbed root of F_e(x)= 0 corresponding to alpha(0)= 5, approximate alpha(epsilon)- 5.

The problem I'm having is that I don't understand what the question is asking.
I tried looking at a few perturbed function question but I can't seem to get it
Phys.Org News Partner Science news on Phys.org
Security CTO to detail Android Fake ID flaw at Black Hat
Huge waves measured for first time in Arctic Ocean
Mysterious molecules in space
lurflurf
#2
Nov20-09, 04:53 PM
HW Helper
P: 2,263
Quote Quote by sprinkle View Post
Consider the polynomial: f(x)= x^5- 300x^3- 126x+ 5005
which has a root alpha= 5. Also consider the perturbed function
F_e(x)= f(x)- epsilon x^5= (1- epsilon)x^5- 300x^3- 126x+ 5005
where epsilon is a small number. Letting alpha(epsilon) denote the perturbed root of F_e(x)= 0 corresponding to alpha(0)= 5, approximate alpha(epsilon)- 5.

The problem I'm having is that I don't understand what the question is asking.
I tried looking at a few perturbed function question but I can't seem to get it
5 is not a root of that equation, perhaps it should be f(x)= x^5- 300x^2- 126x+ 5005?
The idea is since the two polynomials are close the roots should be close
take alpha=5+a epsilon+b epsilon^2+...
find the coefficients


Register to reply

Related Discussions
Perturbed function Calculus 2
How to figure out Perturbed Lagrangians? Advanced Physics Homework 0
Perturbed Harmonic Oscillator Advanced Physics Homework 4
Perturbed Potential Well Advanced Physics Homework 1
Perturbed Harmonic oscil Advanced Physics Homework 0