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From: Oluwa KuIse on 18 May 2010 18:24
Hello.

I'm trying to solve the following set of non-linear simultaneous equations for U and V:
1. U^3 + U*(V^2) = ((a*8*g*h)/f)^2
2. V^3 + V*(U^2) = ((b*8*g*h)/f)^2

Please note that a, b, h, U and V are matrices.
Since this is a cubic equation, I may have a complex conjugate root and a real root. I want to admit (use) only the real roots.
How do I do these two things?
Thanks!
From: Walter Roberson on 18 May 2010 18:32
Oluwa KuIse wrote:

> I'm trying to solve the following set of non-linear simultaneous
> equations for U and V:
> 1. U^3 + U*(V^2) = ((a*8*g*h)/f)^2
> 2. V^3 + V*(U^2) = ((b*8*g*h)/f)^2

> Please note that a, b, h, U and V are matrices.
> Since this is a cubic equation, I may have a complex conjugate root and
> a real root. I want to admit (use) only the real roots.
> How do I do these two things?

The solution *might* be:

[U = 4/f/(b^4+a^4)*(g^2*h^2*f*(b^4+a^4)^2)^(1/3)*a^2,
V = 4/f/(b^4+a^4)*(g^2*h^2*f*(b^4+a^4)^2)^(1/3)*b^2]

However, as I did not work through a matrix solution, the order of the
multiplications is probably wrong.
From: Bruno Luong on 19 May 2010 02:53
Walter Roberson <roberson(a)hushmail.com> wrote in message <hsv4jm$p46$1(a)canopus.cc.umanitoba.ca>...

>
> The solution *might* be:
>
> [U = 4/f/(b^4+a^4)*(g^2*h^2*f*(b^4+a^4)^2)^(1/3)*a^2,
> V = 4/f/(b^4+a^4)*(g^2*h^2*f*(b^4+a^4)^2)^(1/3)*b^2]
>
> However, as I did not work through a matrix solution, the order of the
> multiplications is probably wrong.

To my experience, expression for scalar can't hardly transposed for matrix equation. Typical simple example is

A*X + X*B = C

The solution is NOT X = (A+B) \ C nor X = C / (A+B)

Bruno
From: Bruno Luong on 19 May 2010 03:00
"Oluwa KuIse" <wespeakforex(a)yahoo.com> wrote in message <hsv424$l01$1(a)fred.mathworks.com>...
> Hello.
>
> I'm trying to solve the following set of non-linear simultaneous equations for U and V:
> 1. U^3 + U*(V^2) = ((a*8*g*h)/f)^2
> 2. V^3 + V*(U^2) = ((b*8*g*h)/f)^2
>
> Please note that a, b, h, U and V are matrices.
> Since this is a cubic equation, I may have a complex conjugate root and a real root. I want to admit (use) only the real roots.

You might use FSOLVE is you have opt toolbox.

Bruno
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