Joe

Sep
28
awarded Popular Question
Apr
26
awarded Popular Question
Mar
28
accepted Square root entries of matrices
Mar
28
comment Square root entries of matrices
Hi adam W, Agreed! Intuitively, I thought it would be extremely difficult to do any sort of simplification on this seemimngly innocuous equation and your comments just confirms this! Thanks very much!!
Mar
28
comment Square root entries of matrices
Hi Marvis, please have a look at the question again if you do not mind. I have rewritten it in a more digestible form. Again, given the matrix I posted, how would one go about simplifying this if the entries of the matrices are unknown. Note that the number is a real number.
Mar
28
revised Square root entries of matrices
deleted 232 characters in body
Mar
28
asked Square root entries of matrices
Aug
26
awarded Tumbleweed
Jul
13
comment Singular Perturbation Problem? Asymptotics?
Right! Gosh, this just makes thing a little trickier now. Thanks a bunch!
Jul
13
comment Singular Perturbation Problem? Asymptotics?
Hmm, so what this means is that for $p\in(0,1)$ my boundary conditions wouldn't work and your example illustrates just that. I am tempted to try letting $p=1$ just to see if my boundary condition works. I have a strong feeling the latter will be valid though it might be wrong! Nonetheless, thanks for the helpful comment. You gave me a lot to think about! Edit: You are absolutely right. The boundary conditions do not work, unfortunately even for $p=1$. Why do you think this occur? The equation and boundaries arose from modelling a physical phenomena.
Jul
13
comment Singular Perturbation Problem? Asymptotics?
Hmm, so what this means is that for $p\in(0,1)$ my boundary conditions wouldn't work and your example illustrates just that. I am tempted to try letting $p=1$ just to see if my boundary condition works. I have a strong feeling the latter will be valid though it might be wrong! Nonetheless, thanks for the helpful comment. You gave me a lot to think about!
Jul
12
awarded Supporter
Jul
12
comment Singular Perturbation Problem? Asymptotics?
I see! Thanks for the information!
Jul
12
comment Singular Perturbation Problem? Asymptotics?
@ Andrew WintersWhat do you mean by Gauge Functions? Wiki wasn't very helpful when it comes to this!
Jul
12
comment Singular Perturbation Problem? Asymptotics?
I think I see what you mean. If we choose $p>1$ there is no way to balance out the $\epsilon$ terms whereas if we choose $0<p<1$, we can't balance $\epsilon ^{p}$ apart from when $p=1/2$! Is that what you are saying?
Jul
12
revised Singular Perturbation Problem? Asymptotics?
added 52 characters in body
Jul
12
comment Singular Perturbation Problem? Asymptotics?
Woops!! Yes there are!
Jul
11
revised Singular Perturbation Problem? Asymptotics?
added 32 characters in body
Jul
11
asked Singular Perturbation Problem? Asymptotics?
Jul
11
awarded Commentator
1 2 3