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27m
comment Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
@Calculon, I'm afraid that despite your kind attempts I simply don't know how to utilize them. If you're up to writing a detailed solution that would be extremely appreciated. If it's too much of a hassle I understand and thank you regardless.
1d
comment Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
I have to admit that I simply never saw how to use this sort of technique in order to find moment generating functions. So even though the hints are solid I just don't know how to implement them.
2d
comment Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
Hi Calculon, thanks for your reply. I thought about going in this direction but my problem is that I don't know what the pmf/pdf of the discrete/continuous hitting times are and without those I have no idea how to find the MGF.
2d
asked Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
Feb
27
revised Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
added 1556 characters in body
Feb
26
comment Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
Hey Murp, thanks for your reply! I'm afraid I wasn't able to find any useful way to use the spectral decomposition of $A$ in order to prove these properties (no idea why it was given as a hint), I was however able to additionally prove that the error is monotonically decreasing in the $A$-norm, I will add that to my post later today.
Feb
26
accepted Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
Feb
16
awarded  Promoter
Feb
15
revised Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
added 5 characters in body
Feb
15
revised Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
correction to update formula
Feb
15
revised Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
[Edit removed during grace period]
Feb
14
comment Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
Because $d^{n}$ must be in the column-space of $A$ they can't be in the nullspace. See stackoverflow.com/questions/16703303/… for example. It's easy to show by induction on the update equation that $d^{n}$ are all in the column space.
Feb
14
revised Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
edited body
Feb
14
asked Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
Dec
13
awarded  Yearling
Dec
13
comment Proof that a continuous function from the unit ball to itself without fixed points implies existence of retract from unit ball to unit sphere
Very nice, thanks :)
Dec
13
accepted Proof that a continuous function from the unit ball to itself without fixed points implies existence of retract from unit ball to unit sphere
Dec
13
revised Proof that a continuous function from the unit ball to itself without fixed points implies existence of retract from unit ball to unit sphere
correction following comment
Dec
13
comment Proof that a continuous function from the unit ball to itself without fixed points implies existence of retract from unit ball to unit sphere
Oh that's a good point, I didn't notice that. I will correct the question. Still no idea how to show $a$ is continuous though.
Dec
13
asked Proof that a continuous function from the unit ball to itself without fixed points implies existence of retract from unit ball to unit sphere