Fetching the paper…
Reading the bibliography…
We study the problem of computing the $p\rightarrow q$ norm of a matrix $A \in R^{m \times n}$, defined as \[ \|A\|_{p\rightarrow q} ~:=~ \max_{x \,\in\, R^n \setminus \{0\}} \frac{\|Ax\|_q}{\|x\|_p} \] This problem generalizes the spectral norm of a matrix ($p=q=2$) and the Grothendieck problem ($p=\infty$, $q=1$), and has been widely studied in various regimes.
Résumé de la théorie métrique des produits tensoriels topologiques
Alexandre Grothendieck · 1956
Earlier work this paper cites.
On best lacunary systems of functions
Sergei Borisovich Stechkin · 1961
Earlier work this paper cites.
An application of Fourier methods to the problem of sharpening the Berry-Esseen inequality
Paul van Beek · 1972
Earlier work this paper cites.
Sur la constante de Grothendieck
Jean-Louis Krivine · 1977
Earlier work this paper cites.
The best constants in the khintchine inequality
Uffe Haagerup · 1981
Earlier work this paper cites.
A fast and simple randomized parallel algorithm for the maximal independent set problem
Noga Alon, László Babai, and Alon Itai · 1986
Earlier work this paper cites.
More on embedding subspaces of \ \backslash (l_p \ \backslash ) in \ \backslash (lˆ n_r \ \backslash )
Gideon Schechtman · 1987
Earlier work this paper cites.
A new lower bound on the real Grothendieck constant
JA Reeds · 1991
Earlier work this paper cites.
Semidefinite relaxation and nonconvex quadratic optimization
Yurii Nesterov · 1998
Earlier work this paper cites.
Hardness results for coloring 3-colorable 3-uniform hypergraphs
Subhash Khot · 2002
Earlier work this paper cites.
On non-approximability for quadratic programs
Sanjeev Arora, Eli Berger, Elad Hazan, Guy Kindler, and Muli Safra · 2005
Earlier work this paper cites.
Computation of matrix norms with applications to robust optimization
Daureen Steinberg · 2005
Earlier work this paper cites.
Topics in Banach space theory
Fernando Albiac and Nigel John Kalton · 2006
Cited alongside, same era.
Quadratic forms on graphs
Noga Alon, Konstantin Makarychev, Yury Makarychev, and Assaf Naor · 2006
Cited alongside, same era.
Stable distributions, pseudorandom generators, embeddings, and data stream computation
Piotr Indyk · 2006
Cited alongside, same era.
Two observations regarding embedding subsets of euclidean spaces in normed spaces
Gideon Schechtman · 2006
Cited alongside, same era.
Linear equations modulo 2 and the l_1 diameter of convex bodies
Subhash Khot and Assaf Naor · 2008
Cited alongside, same era.
SDP gaps and UGC-hardness for Max-Cut-Gain
Subhash Khot and Ryan O’Donnell · 2009
Cited alongside, same era.
Grothendieck-type inequalities in combinatorial optimization
Subhash Khot and Assaf Naor · 2012
Later among the works it cites.
Grothendieck’s theorem, past and present
Gilles Pisier · 2012
Later among the works it cites.
Testing product states, quantum Merlin-Arthur games and tensor optimization
Aram W Harrow and Ashley Montanaro · 2013
Later among the works it cites.
Estimating operator norms using covering nets
Fernando GSL Brandao and Aram W Harrow · 2015
Later among the works it cites.
High-dimensional p-norms
Gérard Biau and David M Mason · 2015
Later among the works it cites.
Tight hardness of the non-commutative Grothendieck problem
Jop Briët, Oded Regev, and Rishi Saket · 2015
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Towards computing the Grothendieck constant
Prasad Raghavendra and David Steurer · 2009
Cited alongside, same era.
The UGC hardness threshold of the Lp Grothendieck problem
Guy Kindler, Assaf Naor, and Gideon Schechtman · 2010
Cited alongside, same era.
Graph expansion and the unique games conjecture
Prasad Raghavendra and David Steurer · 2010
Cited alongside, same era.
Hypercontractivity and its applications
Punyashloka Biswal · 2011
Cited alongside, same era.
Approximating matrix p-norms
Aditya Bhaskara and Aravindan Vijayaraghavan · 2011
Cited alongside, same era.
Hypercontractivity, sum-of-squares proofs, and their applications
Boaz Barak, Fernando GSL Brandao, Aram W Harrow, Jonathan Kelner, David Steurer, and Yuan Zhou · 2012
Cited alongside, same era.
Bypassing UGC from some optimal geometric inapproximability results
Venkatesan Guruswami, Prasad Raghavendra, Rishi Saket, and Yi Wu · 2016
Later among the works it cites.
Limitations of semidefinite programs for separable states and entangled games
Aram W Harrow, Anand Natarajan, and Xiaodi Wu · 2016
Later among the works it cites.
Roman Vershynin · 2017
Later among the works it cites.
Approximating operator norms via generalized Krivine rounding
V. Bhattiprolu, M. Ghosh, V. Guruswami, E. Lee, and M. Tulsiani · 2018
Closest in time.
On sketching q q to p p norms
Aditya Krishnan, Sidhanth Mohanty, and David P. Woodruff · 2018
Closest in time.