Spectral Analysis of Matrix Scaling and Operator Scaling

DOI10.1137/20M1315981MaRDI QIDQ4997323

Lap Chi Lau, Akshay Ramachandran, Tsz Chiu Kwok

Publication date: 29 June 2021

Published in: SIAM Journal on Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.03213

zbMATH Keywords

spectral analysisframe theoryoperator scaling

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18)

Cites Work

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• Computational Optimal Transport: With Applications to Data Science
• Hafnians, perfect matchings and Gaussian matrices
• Gaussian kernels have only Gaussian maximizers
• On the existence of equiangular tight frames
• On the scaling of multidimensional matrices
• On a reverse form of the Brascamp-Lieb inequality
• Proof of the van der Waerden conjecture regarding the permanent of a doubly stochastic matrix
• The solution of van der Waerden's problem for permanents
• Convexity properties of the moment mapping
• Completely positive linear maps on complex matrices
• Best constants in Young's inequality, its converse, and its generalization to more than three functions
• Grassmannian frames with applications to coding and communication
• Optimal frames for erasures.
• Algorithmic and optimization aspects of Brascamp-Lieb inequalities, via operator scaling
• A linear lower bound on the unbounded error probabilistic communication complexity.
• Classical complexity and quantum entanglement
• On complexity of matrix scaling
• Convexity properties of the moment mapping. II
• Convexity properties of the moment mapping. III
• Operator scaling: theory and applications
• The Brascamp-Lieb inequalities: Finiteness, structure and extremals
• Perfect matchings in o( n log n ) time in regular bipartite graphs
• Hyperbolic polynomials approach to Van der Waerden/Schrijver-Valiant like conjectures
• Computing the Partition Function for Perfect Matchings in a Hypergraph
• A deterministic polynomial-time algorithm for approximating mixed discriminant and mixed volume
• Designing structured tight frames via an alternating projection method
• Convexity and Commuting Hamiltonians
• On the Complexity of Matrix Balancing
• The Theory of Quantum Information
• Operator scaling via geodesically convex optimization, invariant theory and polynomial identity testing
• The Paulsen problem, continuous operator scaling, and smoothed analysis
• Testing Halfspaces over Rotation-Invariant Distributions
• A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices
• Maximizing determinants under partition constraints
• Envelope Theorems for Arbitrary Choice Sets
• An Introduction to Matrix Concentration Inequalities
• Convexity Properties of Hamiltonian Group Actions