The Kolmogorov N-width for linear transport: exact representation and the influence of the data

• Published in: Advances in computational mathematics Vol. 51; no. 2
• Main Authors: Arbes, Florian, Greif, Constantin, Urban, Karsten
• Format: Journal Article
• Language: English
• Published: New York Springer Nature B.V 01.04.2025
• Subjects: Boundary conditions; Decay rate; Eigenvalues; Eigenvectors; Mathematics; Model reduction; Partial differential equations; Representations; Sobolev space; Trigonometric functions; Upper bounds; Wave equations

The Kolmogorov N -width describes the best possible error one can achieve by elements of an N -dimensional linear space. Its decay has extensively been studied in approximation theory and for the solution of partial differential equations (PDEs). Particular interest has occurred within model order r...