|
|
A matrix is said to be doubly stochastic if its entries are
non-negative, and add up to 1 on each row and each column. Now suppose
I am given a matrix A, and only suppose its entries to be non-negative.
I would like to make it bistochastic by the following procedure :
1) divide each row of A by its sum, this gives a new matrix A' with
noramlized rows
2) divide each column of A' by its sum, to normalize colmuns
3) then repeat alternatively operations 1) and 2), infinitely many
times
How to prove that this procedure converges, and that the limit does not
depend whether one starts with operation (1) or (2) ? This seems to be
true numerically.
Thanks for any hint,
Herve
|
|