6,693 reputation
22349
bio website fph.altervista.org
location Pisa, Italy
age 32
visits member for 5 years, 4 months
seen 13 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.)


1d
revised Lagrangian submanifold of a Calabi-Yau manifold
expanded abbreviation in the title, for clarity
Mar
27
answered Two equivalent descriptions of a physical system yielding a non-trivial mathematical formula
Mar
25
answered The maximal eigenvalue of a symmetric Toeplitz matrix
Mar
24
awarded  Enlightened
Mar
24
awarded  Nice Answer
Mar
24
comment Handling arXiv feeds to avoid duplicates
RSS feeds are updated once per day, too.
Mar
24
answered Automatically generate BibTeX item from arxiv
Mar
23
reviewed Approve hilbert-spaces tag wiki excerpt
Mar
21
reviewed Approve Upper bound for a Selberg-type integral over a rectangular region
Mar
21
reviewed Approve Injective dimension of cyclic modules
Mar
19
answered What are interesting heuristics of determining how far given matrix is from a singular one?
Mar
19
comment What are interesting heuristics of determining how far given matrix is from a singular one?
Why "heuristics"? The two examples that you mention are rigorously defined measures.
Mar
16
comment Rounding errors in images of Julia sets
Please do not post the same question on two SE sites immediately. Crossposting is ok, but only after you did not get a satisfying answer in a few days' time.
Mar
14
reviewed Approve Group laws in class field theory
Mar
14
comment How to calculate one Cauchy type determinant
I don't know about the determinant, but there is some theory on how to compute inverses (and sums and products) of generalized Cauchy matrices. An important quantity is the rank of the numerator (displacement rank), in your case 2. For instance, the inverse of such a matrix (when it exists) will have the same displacement rank. Or there are algorithms to compute their LU decomposition in $O(n^2\cdot \text{(displacement_rank)})$
Mar
13
reviewed Approve Analytic Solution to SDEs
Mar
6
comment Inverse of a matrix expression
$t_i$ is a row vector, I guess? In any case, try applying en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula to get rid of the inverse.
Mar
5
comment Bounds on Hilbert-Schmidt norm of difference of products of matrices
In any case, the proof is a one-liner: the same formula without the norms is an identity (telescoping sum).
Mar
5
revised Bounds on Hilbert-Schmidt norm of difference of products of matrices
added 3 characters in body
Mar
5
comment Bounds on Hilbert-Schmidt norm of difference of products of matrices
@QAMS No, I don't know of a place where that identity and triangle inequality argument appear. For the inequalities combining HS-norm and 2-norm, you can see for instance Hogben, Handbook of Linear Algebra, 37-5 (it is a mammoth-sized book full of facts to cite in linear algebra)