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- W18078851 abstract "Equation (5) with coefficients given by (10) arises from the discretization of an integrodifferential equation appearing in a neutron transport model [100]. The solution of interest is the minimal positive one, whose existence is proved in [100]. Note that for this equation (mathcal{M}) is an M-matrix [70]: in fact, $$mathcal{M} = left[ {begin{array}{*{20}{c}} Gamma &0 0&Delta end{array}} right] - left[ {begin{array}{*{20}{c}} q e end{array}} right]left[ {{e^T} {q^T}} right];$$by Lemma 1.2.2 this is an M-matrix if and only if $$0 leqslant 1 - left[ {{e^T} {q^T}} right]left[ {begin{array}{*{20}{c}} {{Gamma ^{ - 1}}}&0 0&{{Delta ^{ - 1}}} end{array}} right]left[ {begin{array}{*{20}{c}} q e end{array}} right],$$which reduces to $$1 geqslant {e^T}{Gamma ^{ - 1}}q + {q^T}{Delta ^{ - 1}}e = sumlimits_{i = 1}^n {frac{{cleft( {1 - alpha } right)}}{2}} {w_i} + sumlimits_{i = 1}^n {frac{{cleft( {1 + alpha } right)}}{2}} {w_i} = c,$$(8.1.1)in view of (11). According to the terminology in (5.2.2), the equation is nonsingular whenever c ≠ 1, transient when α ≠ 0, c = 1, and null recurrent when α = 0, c = 1." @default.
- W18078851 created "2016-06-24" @default.
- W18078851 creator A5031634329 @default.
- W18078851 date "2011-01-01" @default.
- W18078851 modified "2023-09-25" @default.
- W18078851 title "Newton method for rank-structured algebraic Riccati equations" @default.
- W18078851 doi "https://doi.org/10.1007/978-88-7642-384-0_8" @default.
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