My Math Forum  

Go Back   My Math Forum > Welcome > New Users

New Users Post up here and introduce yourself!


Reply
 
LinkBack Thread Tools Display Modes
May 19th, 2017, 05:27 AM   #1
Newbie
 
Joined: May 2017
From: UAE

Posts: 1
Thanks: 0

Lightbulb Finding roots of multivariable equation

Dears,
I have a set of two equations each of two variables x and y :
f1(x,y) =a1+b1x+c1x^2+...+x^7+a2+b2y+c2y^2+...+y^7+a3xy+b3 x^2y^2+...+x^7y^9.

f2(x,y) =a4+b4x+c4x^2+...+x^7+a5+b5y+c5y^2+...+y^7+a6xy+b6 x^2y^2+...+x^8y^10.

These equations are the partial derivatives of one original equation called Performance Index (J)

I need to find the roots of both equations that equate both of them to zero simultaneously so the solution should be set of pairs points aiming to identify the local minimum and maximum points.

I have managed to find the roots by numeric analysis through Newton Raphson technique with many iterations.

The questions remain:

1) I have managed to find so far four roots that make both equations equal to zero simultaneously, since I have to find the roots one by one through Newton Raphson, when I have to stop saying that these are all possible roots.
3) How many roots we can estimate as a set of solution for above two equations. Is there any rule that we can identify the number of all possible roots?

Thanks in advance.

Last edited by skipjack; May 19th, 2017 at 09:15 AM.
bastha is offline  
 
Reply

  My Math Forum > Welcome > New Users

Tags
equation, finding, multivariable, roots



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Finding approximate values of real roots equation. RKJCHENNAI Abstract Algebra 2 February 20th, 2016 04:25 AM
Finding the equation when givien two roots Mr Davis 97 Algebra 2 March 19th, 2014 08:24 PM
Finding Real Roots of an Equation omarg Calculus 1 October 26th, 2012 04:01 PM
Finding roots of a complex numbers equation nisko Complex Analysis 2 November 6th, 2008 09:52 AM
finding the roots natus zeri Algebra 7 October 21st, 2007 08:29 AM





Copyright © 2017 My Math Forum. All rights reserved.