We know that to express an polynomial as SOS, we can write it as a Matrix SOS

Now we take an example, use SOStools in Matlab to get SOS for $$f(a,b,c)=16(a^2+b^2+c^2)^3-9\left[(a^3+3b^2c)^2+(3ac^2+b^3)^2+(3a^2b+c^3)^2\right]$$ Use the following command

$\text{syms a b c}\\ \text{option.solver = 'sedumi';}\\ \text{p=16*(a^2+b^2+c^2)^3-9*(a^3+3*b^2*c)^2-9*(3*a*c^2+b^3)^2-9*(3*a^2*b+c^3)^2;}\\ \text{[Q,Z]=findsos(p,'rational',option);}$

Then we can found a Matrix SOS.

Now I want to express this Matrix SOS as SOS polynomials (I mean the sum of SOS), how can I do it in Matlab or Maple?

I have read the user's guide, and I found a piece of related information:

enter image description here

But I still don't know how to use this for my problem. Thanks for help!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.