POSITIVE POLYNOMIALS IN SCALAR AND MATRIX VARIABLES, THE SPECTRAL THEOREM AND OPTIMIZATION
By J. William Helton, Mihai Putinar. 2006
59 citations recorded by the source corpus.
We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decomposi- tions, with emphasis on the interaction between classical moment prob- lems, function theory of one or several complex variables and modern operator theory. The second part of the survey focuses on recently dis- covered connections between real algebraic geometry and optimization as well as polynomials in matrix variables and some control theory prob- lems. These new applications have prompted a series of recent studies devoted to the structure of positivity and convexity in a free -algebra, the appropriate setting for analyzing inequalities on polynomials having matrix variables. We sketch some of these developments, add to them and comment on the rapidly growing literature.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/a8fc66b11ebd35ab4907afe3250e5c04e7f464ce
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In Computational Theory and Mathematics
In Control and Systems Engineering
In Numerical Analysis
Citations in the corpus
- Sums of Hermitian Squares and the BMV Conjecture (2007, background): “The following theorem proved in [7] also holds for several variables and motivates the use of sums of hermitian squares (see [ 8 ] for a survey of recent developments).”