Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Kulkarni, Archit"'
Let $G_n$ be an $n \times n$ matrix with real i.i.d. $N(0,1/n)$ entries, let $A$ be a real $n \times n$ matrix with $\Vert A \Vert \le 1$, and let $\gamma \in (0,1)$. We show that with probability $0.99$, $A + \gamma G_n$ has all of its eigenvalue co
Externí odkaz:
http://arxiv.org/abs/2005.08930
Autor:
Garza-Vargas, Jorge, Kulkarni, Archit
We use tools from free probability to study the spectra of Hermitian operators on infinite graphs. Special attention is devoted to universal covering trees of finite graphs. For operators on these graphs we derive a new variational formula for the sp
Externí odkaz:
http://arxiv.org/abs/1912.10137
We exhibit a randomized algorithm which given a matrix $A\in \mathbb{C}^{n\times n}$ with $\|A\|\le 1$ and $\delta>0$, computes with high probability an invertible $V$ and diagonal $D$ such that $\|A-VDV^{-1}\|\le \delta$ using $O(T_{MM}(n)\log^2(n/\
Externí odkaz:
http://arxiv.org/abs/1912.08805
A matrix $A\in\mathbb{C}^{n\times n}$ is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set of nondiagonalizable matrices has measure zero, every $A\in \mathbb{C}^{n\times n}$ is the limit of diagonalizable matrices.
Externí odkaz:
http://arxiv.org/abs/1906.11819
Autor:
Garza-Vargas, Jorge, Kulkarni, Archit
Publikováno v:
SIAM Journal on Matrix Analysis and Applications (2020), 41(3), 1312-1346
We study the Lanczos algorithm where the initial vector is sampled uniformly from $\mathbb{S}^{n-1}$. Let $A$ be an $n \times n$ Hermitian matrix. We show that when run for few iterations, the output of Lanczos on $A$ is almost deterministic. More pr
Externí odkaz:
http://arxiv.org/abs/1904.06012
A sum-dominant set is a finite set $A$ of integers such that $|A+A| > |A-A|$. As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to be rare in some sense. In 2006, however, Martin and O'Bryant showed th
Externí odkaz:
http://arxiv.org/abs/1406.2052
Many fundamental questions in additive number theory (such as Goldbach's conjecture, Fermat's last theorem, and the Twin Primes conjecture) can be expressed in the language of sum and difference sets. As a typical pair of elements contributes one sum
Externí odkaz:
http://arxiv.org/abs/1401.2588
A natural generalization of base B expansions is Zeckendorf's Theorem: every integer can be uniquely written as a sum of non-consecutive Fibonacci numbers $\{F_n\}$, with $F_{n+1} = F_n + F_{n-1}$ and $F_1=1, F_2=2$. If instead we allow the coefficie
Externí odkaz:
http://arxiv.org/abs/1309.5600
Autor:
Demontigny, Philippe, Do, Thao, Kulkarni, Archit, Miller, Steven J., Moon, David, Varma, Umang
Publikováno v:
Journal of Number Theory, Volume 141 (2014), 136--158
A beautiful theorem of Zeckendorf states that every positive integer can be uniquely decomposed as a sum of non-consecutive Fibonacci numbers $\{F_n\}$, where $F_1 = 1$, $F_2 = 2$ and $F_{n+1} = F_n + F_{n-1}$. For general recurrences $\{G_n\}$ with
Externí odkaz:
http://arxiv.org/abs/1309.5599
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