Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2009.49.4.595
Title & Authors
Riccati Equation and Positivity of Operator Matrices Fujii, Jun Ichi; Fujii, Masatoshi; Nakamoto, Ritsuo;
We show that for an algebraic Riccati equation , its solutions are given by X = W + BT for some solution W of = . To generalize this, we give an equivalent condition for for given positive operators B and A, by which it can be regarded as Riccati inequality . As an application, the harmonic mean B ! C is explicitly written even if B and C are noninvertible.
Riccati equation;operator matrix;geometric mean and harmonic mean;
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