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?







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  • What matrix norm are you using?
    – Rodrigo de Azevedo
    Aug 17 at 7:08














up vote
1
down vote

favorite
3












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?







share|cite|improve this question






















  • What matrix norm are you using?
    – Rodrigo de Azevedo
    Aug 17 at 7:08












up vote
1
down vote

favorite
3









up vote
1
down vote

favorite
3






3





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?







share|cite|improve this question














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?









share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 17 at 7:06









Rodrigo de Azevedo

12.6k41751




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asked May 22 at 11:09









tchnvkng

62




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  • What matrix norm are you using?
    – Rodrigo de Azevedo
    Aug 17 at 7:08
















  • What matrix norm are you using?
    – Rodrigo de Azevedo
    Aug 17 at 7:08















What matrix norm are you using?
– Rodrigo de Azevedo
Aug 17 at 7:08




What matrix norm are you using?
– Rodrigo de Azevedo
Aug 17 at 7:08















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