Solution of Quadratic Matrix Equation

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Neilabh Banzal 2022-2-24

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评论： Benjamin Thompson 2022-2-25

Hello!

I want to solve a Quadratic Matrix Equation of the form -

Solve for z: z' A z + B' z + D = 0

I did see a similar question here and David Goodmanson has an excellent answer for the z' C z + z + D = 0. However, I don't understand how he came up with the closed form solution or how to generalize it for my case. Any help would be greatly appreciated.

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Neilabh Banzal 2022-2-25

I was trying to avoid using fsolve as I have to call it repeatedly. Is there no other way?

Torsten 2022-2-25

编辑：Torsten 2022-2-25

Maybe - if you tell us how you plan to evaluate A*z to get a 6x6-matrix.

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回答（2 个）

Benjamin Thompson 2022-2-24

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icare and idare are used to numerically solve the continuous or discrete forms of the Riccati equation.

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Neilabh Banzal 2022-2-25

@Benjamin Thompson, this is not a Riccati Equation. Note that there is a B' z term, but no z' B term.

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Benjamin Thompson 2022-2-25

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You could look at this work on File Exchange:

https://www.mathworks.com/matlabcentral/fileexchange/26956-solve-bilateral-matrix-quadratic-equation?s_tid=srchtitle

Then you run it 6 times for each of the 6 6x6 matrices in the 6x6x6 A matrix. If you have specific values to post for your problem in a MAT file, please do so.