Results 31 to 40 of about 1,217,124 (142)

Kronecker Product Approximation of Operators in Spectral Norm via Alternating SDP

, 2023
The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling.
Dressler, Mareike, Chandrasekaran, Venkat, Uschmajew, André   +2 more
core   +2 more sources

On the structure of boolean functions with small spectral norm [PDF]

Proceedings of the 5th conference on Innovations in theoretical computer science, 2014
In this paper we prove results regarding Boolean functions with small spectral norm (the spectral norm of f is $\|\hat{f}\|_1=\sum_α|\hat{f}(α)|$). Specifically, we prove the following results for functions $f:\{0,1\}^n \to \{0,1\}$ with $\|\hat{f}\|_1=A$. 1. There is a subspace $V$ of co-dimension at most $A^2$ such that $f|_V$ is constant. 2.
Amir Shpilka, Avishay Tal, Ben lee Volk
openaire   +6 more sources

The Spectral Norm of Finite Functions

, 1991
In many recent results in learning and computational complexity theory which rely on Fourier analysis, the spectral norm plays a key role. An understanding of this quantity would appear to be useful in both gauging and exploiting these results, and in understanding the underlying techniques.
Bellare, Mihir
openaire   +2 more sources

Some results on geometric circulant matrices involving the Leonardo numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In this study, by the motivation of the papers in the literature, we construct a special geometric circulant matrix Leᵣ* whose entries are the Leonardo numbers. Then, we investigate some linear algebraic properties of these matrices.
Samet Arpacı, Fatih Yılmaz
doaj   +1 more source

Analysis and methodology of determining the norm of eigenfunctions as a limit transition in the scalar product in the spectral Stourm-Louvile problem for a photonic one-dimensional crystal

Вісник Харківського національногоуніверситету імені В.Н. Каразіна. Серія: Радіофізика та електроніка, 2023
Relevance The last of the decades (approximately from the 90s of the 20th century) to rapid grow of photonics. That's why, firstly, relevance this work is related to relevance diffraction problems for the structures of optics ranges (photonic crystal ...
О.V. Kazanko, О.E. Penkina
doaj   +1 more source

Spectral Embedding Norm [PDF]

, 2021
Anomaly detection is a data partitioning algorithm which separates outliers from normative data points. An unsupervised learning approach to this problem does not assume any prior information.
Dror, Shahar
core   +1 more source

On the spectral norm of r-circulant matrices with the Pell and Pell-Lucas numbers

Journal of Inequalities and Applications, 2016
Let us define A = C r ( a 0 , a 1 , … , a n − 1 ) $A=C_{r}(a_{0},a_{1},\ldots,a_{n-1})$ to be a n × n $n \times n$ r-circulant matrix. The entries in the first row of A = C r ( a 0 , a 1 , … , a n − 1 ) $A=C_{r}(a_{0},a_{1},\ldots,a_{n-1})$ are a i = P i
Ramazan Türkmen, Hasan Gökbaş
doaj   +1 more source

Gap Between Operator Norm and Spectral Radius for the Square of Antidiagonal Block Operator Matrices

Communications in Advanced Mathematical Sciences, 2022
In this work, the gap between operator norm and spectral radius for the square of antidiagonal block operator matrices in the direct sum of Banach spaces has been investigated, and also the gap between operator norm and numerical radius for the square of
Elif Otkun Çevik
doaj   +1 more source

Maps preserving spectral radius, numerical radius, spectral norm [PDF]

, 2007
Characterizations are obtained for Schur (Hadamard) multiplicative maps on complex matrices preserving the spectral radius, numerical radius, or spectral norm. Similar results areobtained for maps under weaker assumptions. Furthermore, a characterization
Li, Chi-Kwong, Poon, Edward, Rastogi, Ashwin   +2 more
core   +1 more source

Relative Spectral Norm on Algebraic Numbers

Rendiconti del Seminario Matematico della Università di Padova, 2009
Summary: Let \(K\) be a subfield of \(\overline{\mathbb Q}\), a fixed algebraic closure of \(\mathbb Q\), the field of rational numbers. Let \(G_K = \mathrm{Gal}(\overline{\mathbb Q}/K)\) be the absolute Galois group of \(K\). For any \(x \in \overline{\mathbb Q}\), we consider the \(K\)-spectral norm: \(\| x \|_K = \max\{|\sigma(x)| : \sigma \in G_K\}\
Popescu, Angel, Sultana, Sobia
openaire   +3 more sources