2022/12/13 by Nam Van Tran, Van Tran, Nam, Imme van den Berg +1
Mathematics · #03H05 #15A03 #15A09 #15B33 #65F99 #Algorithm #Applied mathematics #Coefficient matrix #Computer science #FOS: Mathematics #Gaussian #Gaussian elimination #Geometry #Linear algebra #Linear system #Mathematical analysis #Mathematical and Theoretical Analysis #Mathematics #Numerical Analysis (math.NA) #Robustness (evolution)
paper · pdf · doi:10.48550/arxiv.2302.12763
openalex publication_date 2022/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Flexible systems are linear systems of inclusions in which the elements of the coefficient matrix are external numbers in the sense of nonstandard analysis. External numbers represent real numbers with small, individual error terms. Using Gaussian elimination, a flexible system can be put into a row-echelon form with increasing error terms at the right-hand side. Then parameters are assigned to the error terms and the resulting system is solved by common methods of linear algebra. The solution set may have indeterminacy not only in terms of linear spaces, but also of modules. We determine maximal robustness for flexible systems.