95 reputation
6
bio website
location
age
visits member for 1 year, 9 months
seen Sep 17 at 16:52

Jun
17
accepted A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices
Jun
15
answered A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices
May
19
revised A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices
deleted 272 characters in body
May
17
awarded  Nice Question
May
17
comment A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices
@user1551, it only happens for larger $n$ and very large $k$. Although, for $k$ which is relatively small to $n$, it does not exceed $3$ even for large $n$. It might have something to do with the accuracy of the "funm" function rather than to the result itself. I have no intuition as to why it should not be uniformly bounded.
May
16
comment A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices
@StephenMontgomery-Smith, thank you for your comment. Trying to derive an analytic expression, even though the diagonalization is explicitly known, was not successful. However, I did try random symmtric stochastic circulant matrices in Matalb, and for $k = O(\log n)$ the results were indeed small. However, for larger $k$ (which I am not interested), the results did exceed $3$. Any other insight would be helpful, as I am trying to show that under some (maybe more) constraints I can bound the infinity norm of $\frac{1}{T}\sum_{k=1}^{T}\cos(kA)$ by a constant, for $T = O(\log n)$.
May
13
comment A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices
@user1551, in case $A$ is the $2 \times 2$ matrix $[a,1-a;1-a, a]$, the infinity norm is given by $\max\{|\cos(k)|,|\cos((2a-1)k)|\}$. And indeed, as you stated, the maximum is obtained for $a=0.5$, which corresponds to your assumption. Unfortunately, I had no further insight. Thank you.
May
8
revised A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices
alternative formulation
May
5
revised A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices
added 4 characters in body
May
5
revised A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices
added explainations
May
5
asked A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices
Mar
22
awarded  Teacher
Mar
22
answered Asymptotics of Gelfand's formula
Mar
18
awarded  Supporter
Mar
18
comment Asymptotics of Gelfand's formula
Indeed, thank you. However, it did imply that there is a more concrete expression than the usual: $\forall \epsilon \exists N \forall k \ge N. \|A^k\| < (\rho(A)+\epsilon)^{k}$. Specifically, the relations between those constants. Are you aware of any?
Mar
18
revised Asymptotics of Gelfand's formula
added 8 characters in body
Mar
18
revised Asymptotics of Gelfand's formula
deleted 11 characters in body
Mar
18
asked Asymptotics of Gelfand's formula
Feb
25
comment Rate of convergence of Fourier series
Of course, I will rephrase. Is there a result not involving the Lipschitz constant?
Feb
25
asked Rate of convergence of Fourier series