6,970 reputation
22351
bio website fph.altervista.org
location Pisa, Italy
age 32
visits member for 5 years, 7 months
seen 3 mins ago

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

(This profile was written for Mathoverflow, but Stack Exchange insists on copying it over verbatim to other sites, where it makes less sense.)


Jul
1
reviewed Approve A conjecture on the prime counting function
Jun
28
comment all paths between two nodes of an grid structure
From the added image, it looks like an informatics Olympiad problem.
Jun
28
reviewed Approve all paths between two nodes of an grid structure
Jun
25
comment Can I find the gap between the two least eigenvalues of this special matrix A(t)?‎
Are all the values inside the band equal to $ct+d$, or can there be zeros also inside the band?
Jun
25
answered Find inverse and determinant of a symmetric matrix - for a maximum-likelihood estimation
Jun
23
comment Prove or disprove a matrix logarithm equation
I am not a differential geometer, but after reading the formulation in your other question, I am more convinced that it can't be done, at least with a reasonably smooth function. What you ask for is a distance-preserving isomorphism between $\mathbb{S}^n_+$ and $\mathbb{R}^{n^2}$, and this shouldn't be possible because they have different curvature.
Jun
23
comment Prove or disprove a matrix logarithm equation
What do you mean by "treated"? Matlab, Mathematica and Python (sympy) all have library functions to compute matrix logarithms without trouble.
Jun
23
comment Prove or disprove a matrix logarithm equation
Have you done some numerical experiments? In particular, testing longer chains such as $(P-Q)+(Q-R)+(R-S)=(P-S)$.
Jun
20
comment Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Aren't the two axioms equivalent? One can extend (2) to three disjoint sets and then apply it to $P\cap Q$, $P\setminus Q$ and $Q\setminus P$
Jun
15
reviewed Approve combinatorics-on-words tag wiki
Jun
15
reviewed Approve combinatorics-on-words tag wiki excerpt
Jun
14
reviewed Approve Suggestions for dealing with the “timed” balls-into-bins model
Jun
12
comment Interesting relationships between Cholesky decomposition and diagonalization
Sorry, that was badly phrased from my side. I don't mean that one is intrinsically more stable than the other (they are both backward stable), but that if you go through an additional step (eigendecomposition -> Cholesky -> whatever you need, correlated variables for instance) then it is less stable than doing it directly skipping a step.
Jun
11
comment The 2-norm of a positive circulant matrix
What you ask here is basically the content of my comment in the other question you linked to. The proof in my reference is essentially @YemonChoi's argument.
Jun
8
answered arg min_X ||A X B - C||^2, with X diagonal
Jun
7
revised Finding the distribution of a random variable numerically with sample data?
edited body
Jun
7
reviewed Approve independence-results tag wiki excerpt
Jun
7
revised Finding the distribution of a random variable numerically with sample data?
added 284 characters in body
Jun
7
answered Finding the distribution of a random variable numerically with sample data?
Jun
7
comment Finding the distribution of a random variable numerically with sample data?
What are "discrete data points"? Random samples? Or values of the pdf at some prescribed points?