Riccati Equation and Positivity of Operator Matrices
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We show that for an algebraic Riccati equation [수식], its solutions are given by X = W + BT for some solution [수식], To generalize this, we give an equivalent condition for [수식] for given positive operators B and A, by which it can be regarded as Riccati inequality [수식]. As an application, the harmonic mean B ! C is explicitly written even if B and C are noninvertible.
Abstract
We show that for an algebraic Riccati equation [수식], its solutions are given by X = W + BT for some solution [수식], To generalize this, we give an equivalent condition for [수식] for given positive operators B and A, by which it can be regarded as Riccati inequality [수식]. As an application, the harmonic mean B ! C is explicitly written even if B and C are noninvertible.
참고문헌 (12)
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