Decompose stochastic matrix in product of two stochastic matrices
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There exist stochastic matrices $Q$ such that there is no stochastic matrix $P$ such that $P^2=Q$.
I am interested in the following problem:
For a given stochastic matrix $Q$, find stochastic matrices $P_1$ and $P_2$ that minimize $|P_ 1-P_2|$ such that $P_1 P_2 = Q$.
Does anybody know of references or has ideas on how to tackle this?
matrices markov-chains matrix-decomposition stochastic-matrices
add a comment |Â
up vote
1
down vote
favorite
There exist stochastic matrices $Q$ such that there is no stochastic matrix $P$ such that $P^2=Q$.
I am interested in the following problem:
For a given stochastic matrix $Q$, find stochastic matrices $P_1$ and $P_2$ that minimize $|P_ 1-P_2|$ such that $P_1 P_2 = Q$.
Does anybody know of references or has ideas on how to tackle this?
matrices markov-chains matrix-decomposition stochastic-matrices
What matrix norm are you using?
â Rodrigo de Azevedo
Aug 17 at 7:08
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
There exist stochastic matrices $Q$ such that there is no stochastic matrix $P$ such that $P^2=Q$.
I am interested in the following problem:
For a given stochastic matrix $Q$, find stochastic matrices $P_1$ and $P_2$ that minimize $|P_ 1-P_2|$ such that $P_1 P_2 = Q$.
Does anybody know of references or has ideas on how to tackle this?
matrices markov-chains matrix-decomposition stochastic-matrices
There exist stochastic matrices $Q$ such that there is no stochastic matrix $P$ such that $P^2=Q$.
I am interested in the following problem:
For a given stochastic matrix $Q$, find stochastic matrices $P_1$ and $P_2$ that minimize $|P_ 1-P_2|$ such that $P_1 P_2 = Q$.
Does anybody know of references or has ideas on how to tackle this?
matrices markov-chains matrix-decomposition stochastic-matrices
edited Aug 17 at 7:06
Rodrigo de Azevedo
12.6k41751
12.6k41751
asked May 22 at 11:09
tchnvkng
62
62
What matrix norm are you using?
â Rodrigo de Azevedo
Aug 17 at 7:08
add a comment |Â
What matrix norm are you using?
â Rodrigo de Azevedo
Aug 17 at 7:08
What matrix norm are you using?
â Rodrigo de Azevedo
Aug 17 at 7:08
What matrix norm are you using?
â Rodrigo de Azevedo
Aug 17 at 7:08
add a comment |Â
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What matrix norm are you using?
â Rodrigo de Azevedo
Aug 17 at 7:08