Given the matrix equation AX+XB+f(X)C=D in the unknown n×m matrix X, we analyze existence and uniqueness conditions, together with computational solution strategies for f:Rn×m→R being a linear or nonlinear function. We characterize different properties of the matrix equation and of its solution, depending on the considered classes of functions f. Our analysis mainly concerns small dimensional problems, though several considerations also apply to large scale matrix equations.
Numerical solution of a class of quasi-linear matrix equations / Porcelli M.; Simoncini V.. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - STAMPA. - 664:(2023), pp. 349-368. [10.1016/j.laa.2023.01.024]
Numerical solution of a class of quasi-linear matrix equations
Porcelli M.;
2023
Abstract
Given the matrix equation AX+XB+f(X)C=D in the unknown n×m matrix X, we analyze existence and uniqueness conditions, together with computational solution strategies for f:Rn×m→R being a linear or nonlinear function. We characterize different properties of the matrix equation and of its solution, depending on the considered classes of functions f. Our analysis mainly concerns small dimensional problems, though several considerations also apply to large scale matrix equations.File | Dimensione | Formato | |
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