5,657 reputation
22140
bio website fph.altervista.org
location Pisa, Italy
age 31
visits member for 4 years, 9 months
seen 1 hour ago

Numerical linear algebra. Mainly matrix equations and their applications (control theory, applied probability).


3h
revised Proving that the eigenvalues of a certain matrix product are positive
added 21 characters in body
4h
answered Proving that the eigenvalues of a certain matrix product are positive
22h
comment Estimating the volume of a union of balls
The other problem is that convergence is very slow -- if you want more than a couple of correct digits, it might take quite long even on a modern computer.
1d
reviewed Approve suggested edit on A question on $p$-approximation property
2d
answered Adjusting matrix in generalized eigenvalue problem for the design of eigenfunctions
2d
comment Adjusting matrix in generalized eigenvalue problem for the design of eigenfunctions
@JoonasIlmavirta Wiki: generalized eigenproblem should make the setting clearer and answer your first two questions. I second the third one though: what kind of modifications? What kind of properties? This looks too general; can you be more specific or make an example?
2d
comment Block Matrix determinant
Diagonalize $1_k$.
Aug
24
comment open problems in Numerical Analysis
I don't like the adjective "good open problems". If you replace it with "famous, long-standing and important" this would make a reasonable question in my view.
Aug
23
comment Something like mathoverflow in other sciences
Someone added physicsoverflow, but it doesn't "run on the same platform as Math Overflow". The introduction should be changed to refer to that, I think -- it doesn't really matter if a site uses SE rather than q2a as software backend.
Aug
22
comment Smith Normal Form for block matrix
What kind of results? Special properties of the Smith form in that case? Efficient computation? A "block-Smith" variant that works on the matrix ring of $k\times k$ matrices?
Aug
21
comment Is there an easy way to tell if all eigenvalues of a unitary or self-adjoint matrix only have eigenvalues of multiplicity two?
Are you interested in an algorithm to run on a computer or in a theoretical tool? If the former, do you want an exact result (all computations with big integers or exact rationals) or are you fine with an implementation based on floating point numbers?
Aug
19
answered Why are there so few zero-dimensional polynomial system solvers and is this because there is no real market for them?
Aug
12
revised How do functions operate in a Sobolev space $H^{s}$?
fixed grammar
Aug
8
comment Top specialized journals
Num Math and Math Comp are more generalist; SIAM has several journals with different scopes, but all of them rank among the top ones. In particular, SIAM Review, which mostly publishes reviews and article of interest to a broad range of researchers, and has an impressive impact factor.
Aug
5
comment On the solution of a generalized Lyapunov equation
For the record, $\|F_i\otimes F_i\|=\|F_i\|^2$, so this should coincide with the bound mentioned in the comments.
Aug
5
comment On the solution of a generalized Lyapunov equation
@JorisBierkens I did not know of this discussion, thanks for pointing it out. On the other hand, I find your sarcastic "thank you" slightly out of line; a simple link would have been sufficient.
Aug
5
comment On the solution of a generalized Lyapunov equation
It is unusual (and frowned upon) to thank other users in questions on this site, so I have removed a couple of sentences from your post. Back to business now: you say that it is 'clear' that $X$ is positive definite under those conditions; based on what exactly? The usual criterion for positive-definiteness in the Lyapunov case ($B=A^T$, one term) is that all the eigenvalues of $A$ have negative real part, which seem different from (and contradicting with) with your proposed one.
Aug
5
revised On the solution of a generalized Lyapunov equation
removed thanks; tried to make the text flow a bit better
Aug
4
reviewed Approve suggested edit on Why are they called Specht Modules?
Aug
3
accepted Sensitivity of the range of a matrix