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Thus, we have to investigate the payments of the defaulting banks and the corresponding price of the illiquid asset, defined by the maximal solution to Eqs. (4) and (5).
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Guo [Numerical solution of a quadratic eigenvalue problem, Linear Algebra and its Applications 385 (2004) 391 406] showed that all eigenvalues of the QEP can be found by solving the maximal solution of a nonlinear matrix equation Z+A⊤Z-1A="Q with quadratic convergence when the QEP has no eigenvalues on the imaginary axis.
Take ( λ 0, ψ 0 ) ∈ D and denote, for simplicity, by x 0 the maximal solution x ( λ 0, ψ 0 ˜ ) of (3.3) corresponding to ( λ 0, ψ 0 ˜ ).
Moreover, (x,y) is the maximal solution to these equations by construction.
In this case, we only consider the maximal solution, which can be obtained by standard regularized approximation methods.
Step 3. X* is the maximal solution of problem (1) in S. By the definition of Φ we have u* is a solution for the problem (1).
This is the maximal solution.
This solution is called the maximal solution.
Clearly, the comparison principle is valid for the maximal solution.
where ω is the maximal solution to (25).
where r ( t ) is the maximal solution of (3.5).
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