l*****y
发帖数: 5 | 1 I have such type of matrix problems: An unknow matrix X \in R^{nxn} satisfies
an equation with X in quadratic form (power to two). For example, X is real
symmetric and the equation is:
( P * X * P' + Q ) = X * R * (P * X * P' + Q ) + X
P, Q, and R are given constant matrices. My question is: what is the approach
to generally solve such type of equations? it is really a simple quadratic
equation for any scalar X (middle school problem). But how about if X is an
unknown matrix? Is such type of mat | e****r
发帖数: 166 | 2 did you check any interation method books? i think if X is also a sparse
matrix, the problem will be more easy to solve.
satisfies
approach
【在 l*****y 的大作中提到】
: I have such type of matrix problems: An unknow matrix X \in R^{nxn} satisfies
: an equation with X in quadratic form (power to two). For example, X is real
: symmetric and the equation is:
: ( P * X * P' + Q ) = X * R * (P * X * P' + Q ) + X
: P, Q, and R are given constant matrices. My question is: what is the approach
: to generally solve such type of equations? it is really a simple quadratic
: equation for any scalar X (middle school problem). But how about if X is an
: unknown matrix? Is such type of mat
| l*****y
发帖数: 5 | 3 Thanks for your response.
My original intention was not to get the numerical solution to this equation,
since I was doing some theoretical analysis. I was trying to get the general
analytic solution. I already learned that no such general analytic solutions
to this type of equations.
I apologize that I didn't state the problem clearly.
real
an
【在 e****r 的大作中提到】
: did you check any interation method books? i think if X is also a sparse
: matrix, the problem will be more easy to solve.
:
: satisfies
: approach
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