How to solve the equation $XE+EX^{*}=P$
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Suppose X is a lower triangular matrix having the form
$$X=
begin{bmatrix}
x_{0}\
x_{1}&x_{0}\
vdots&ddots&ddots\
x_{n}&cdots&x_{1}&x_{0}
end{bmatrix}
$$
and $E$ is a positive definite matrix. Given $P>0$ and $E>0$, how to solve the equation
$$XE+EX^{*}=P$$
matrices systems-of-equations
asked Nov 17 at 8:07
Yufang Cui
233
add a comment |
up vote
2
down vote
favorite
Suppose X is a lower triangular matrix having the form
$$X=
begin{bmatrix}
x_{0}\
x_{1}&x_{0}\
vdots&ddots&ddots\
x_{n}&cdots&x_{1}&x_{0}
end{bmatrix}
$$
and $E$ is a positive definite matrix. Given $P>0$ and $E>0$, how to solve the equation
$$XE+EX^{*}=P$$
matrices systems-of-equations
asked Nov 17 at 8:07
Yufang Cui
233
It should be a system of linear equations which can be solved using Gaussian Elimination. Try it with $n=1$ or $n=2$.
– Axel Kemper
Nov 17 at 12:33
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Suppose X is a lower triangular matrix having the form
$$X=
begin{bmatrix}
x_{0}\
x_{1}&x_{0}\
vdots&ddots&ddots\
x_{n}&cdots&x_{1}&x_{0}
end{bmatrix}
$$
and $E$ is a positive definite matrix. Given $P>0$ and $E>0$, how to solve the equation
$$XE+EX^{*}=P$$
matrices systems-of-equations
asked Nov 17 at 8:07
Yufang Cui
233
Suppose X is a lower triangular matrix having the form
$$X=
begin{bmatrix}
x_{0}\
x_{1}&x_{0}\
vdots&ddots&ddots\
x_{n}&cdots&x_{1}&x_{0}
end{bmatrix}
$$
and $E$ is a positive definite matrix. Given $P>0$ and $E>0$, how to solve the equation
$$XE+EX^{*}=P$$
matrices systems-of-equations
matrices systems-of-equations
asked Nov 17 at 8:07
Yufang Cui
233
asked Nov 17 at 8:07
Yufang Cui
233
asked Nov 17 at 8:07
Yufang Cui
233
asked Nov 17 at 8:07
Yufang Cui
233
asked Nov 17 at 8:07
Yufang Cui
233
233
It should be a system of linear equations which can be solved using Gaussian Elimination. Try it with $n=1$ or $n=2$.
– Axel Kemper
Nov 17 at 12:33
add a comment |
It should be a system of linear equations which can be solved using Gaussian Elimination. Try it with $n=1$ or $n=2$.
– Axel Kemper
Nov 17 at 12:33
It should be a system of linear equations which can be solved using Gaussian Elimination. Try it with $n=1$ or $n=2$.
– Axel Kemper
Nov 17 at 12:33
It should be a system of linear equations which can be solved using Gaussian Elimination. Try it with $n=1$ or $n=2$.
– Axel Kemper
Nov 17 at 12:33
add a comment |
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It should be a system of linear equations which can be solved using Gaussian Elimination. Try it with $n=1$ or $n=2$.
– Axel Kemper
Nov 17 at 12:33