Abstract
Recently there has been a surge of activity on “scaling” algorithms. These include matrix scaling, operator scaling, uniform and non-uniform tensor scaling. These have a variety of applications in a number of diverse areas such as statistics, numerical linear algebra, non-commutative algebra, and derandomization, invariant theory, functional analysis and combinatorial geometry. These algorithms are typically from the alternating minimization (AM) class and the analysis uses tools from invariant theory and representation theory.
I plan to survey some of these scaling algorithms with a focus on the algebraic nature of their analysis.