We are interested in algebraic properties of the solution X to the linear or mildly nonlinear symmetric matrix equation AX+XA+UΦ(X)UT+BBT=0 with symmetric A. We analyze monotonicity and low-rank properties of closed form solutions, whenever available, with respect to the solution of the equation AX+XA+BBT=0. We extend this analysis to approximation recurrences, for which monotonicity and singular value decay properties are discussed.
Simoncini, V. (2025). Algebraic properties of solutions to certain nonlinear matrix equations. LINEAR ALGEBRA AND ITS APPLICATIONS, 1, 1-22 [10.1016/j.laa.2025.09.017].
Algebraic properties of solutions to certain nonlinear matrix equations
Simoncini V.
2025
Abstract
We are interested in algebraic properties of the solution X to the linear or mildly nonlinear symmetric matrix equation AX+XA+UΦ(X)UT+BBT=0 with symmetric A. We analyze monotonicity and low-rank properties of closed form solutions, whenever available, with respect to the solution of the equation AX+XA+BBT=0. We extend this analysis to approximation recurrences, for which monotonicity and singular value decay properties are discussed.File in questo prodotto:
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