Numerical solution of a class of quasi-linear matrix equations

2022/09/02 by Margherita Porcelli, Valeria Simoncini, Porcelli, Margherita +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2209.00897

openalex publication_date 2022/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given the matrix equation \bf A X + \bf X B + f(\bf X ) \bf C =\bf D in the unknown n× m matrix \bf X , we analyze existence and uniqueness conditions, together with computational solution strategies for f : ℝ^{n × 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.

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