Operator-valued Semicircular Elements: Solving A Quadratic Matrix Equation with Positivity Constraints

Abstract

We show that the quadratic matrix equation VW + η(W )W = I, for given V with positive real part and given analytic mapping η with some positivity preserving properties, has exactly one solution W with positive real part. Also we provide and compare numerical algorithms based on the iteration underlying our proofs. This work bears on operator-valued free… (More)

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Cite this paper

@inproceedings{Helton2007OperatorvaluedSE, title={Operator-valued Semicircular Elements: Solving A Quadratic Matrix Equation with Positivity Constraints}, author={J. William Helton}, year={2007} }