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Results tagged with recurrences
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user 62673
7
votes
3
answers
512
views
Trace of a nonlinear matrix equation (cont'd)
Let $X_0$ be a trace-one positive definite matrix, i.e. $X_0>0$, $\mathrm{tr}(X_0)=1$. Let $A>0$ and consider the following iteration
$$
X_{k+1} = X_k^{1/2}AX_k^{1/2},\quad k\geq 0,\quad (\star)
$$
wh …
- 2,712
5
votes
1
answer
395
views
Trace of a nonlinear matrix equation
Let $X_0$ be a trace-one positive definite matrix, i.e. $X_0>0$, $\mathrm{tr}(X_0)=1$. Let $A>0$ and consider the following iteration
$$
X_{k+1} = X_k^{1/2}AX_k^{1/2},\quad k\geq 0,\quad (\star)
$$
wh …
- 2,712
2
votes
Trace of a nonlinear matrix equation (cont'd)
I sketch here a solution for the $2\times 2$ case. My hope is that the outlined approach can be used to find a general solution.
As noticed in Addendum 1, we can restrict wlog to diagonal positive de …
- 2,712