Under certain conditions, an element of a tensor product space can be identified with a compact operator and the singular value decomposition (SVD) applies to the latter. These conditions are not fulfilled in Sobolev spaces. In the previous part of this work (part I) [Z. Anal. Anwend. 39 (2020), 349–369], we introduced some preliminary notions in the theory of tensor product spaces. We analyzed low-rank approximations in and the error of the SVD performed in the ambient space. In this work (part II), we continue by considering variants of the SVD in norms stronger than the H^1 H^1 H^1$-functions. Finally, we provide a few numerical examples that support our theoretical findings.
Cite this article
Mazen Ali, Anthony Nouy, Singular Value Decomposition in Sobolev Spaces: Part II. Z. Anal. Anwend. 39 (2020), no. 4, pp. 371–394DOI 10.4171/ZAA/1664