Spectral Analysis of Matrix Scaling and Operator Scaling

Explore the intricacies of spectral analysis in matrix and operator scaling in this 20-minute IEEE conference talk. Delve into topics such as alternating scaling algorithms, continuous matrix and operator scaling algorithms, gradient flow, and spectral conditions. Learn about the main theorem of linear convergence, condition numbers, frames, and the Paulsen problem. Discover applications, previous work in the field, frame results, and permanent open questions. Gain insights from speakers Tsz Chiu Kwok, Lap Chi Lau, and Akshay Ramachandran as they present their findings and discuss the numerical relaxation techniques used in this area of study.

Intro
Outline
Alternating Scaling Algorithm
Applications
Continuous Matrix Scaling Algorithm
Continuous Operator Scaling Algorithm
Gradient Flow
Spectral Condition for Matrix Scaling
Spectral Condition for Operator Scaling
Main Theorem: Linear Convergence
Condition Number
Frames
Numerical Relacation
The Paulsen Problem
Previous work
Frame Results
Permanent
Open Questions