Tree-based tensor formats

Bachmayr, M., Schneider, R., Uschmajew, A.: Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations. Found. Comput. Math. 16, 1423–1472 (2016)

Falcó, A., Hackbusch, W., Nouy, A.: On the Dirac–Frenkel variational principle on tensor Banach spaces. Found. Comput. Math. (2018). https://doi.org/10.1007/s10208-018-9381-4

Falcó, A., Hackbusch, W.: Minimal subspaces in tensor representations. Found. Comput. Math. 12, 765–803 (2012)

Falcó, A., Nouy, A.: Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces. Numer. Math. 121, 503–530 (2012)

Grasedyck, L., Kressner, D., Tobler, C.: A literature survey of low-rank tensor approximation techniques. GAMM-Mitt. 36(1), 53–78 (2013)

Greub, W.H.: Linear Algebra. Graduate Text in Mathematics, 4th edn. Springer, Berlin (1981)

Grothendieck, A.: Résumé de la th éorie métrique des produit tensoriels topologiques. Bol. Soc. Mat. S ão Paulo 8, 1-79 (1953/56)

Hackbusch, W., Kühn, S.: A new scheme for the tensor representation. J. Fourier Anal. Appl. 15, 706–722 (2009)

Hackbusch, W.: Tensor Spaces and Numerical Tensor Calculus. Springer, Berlin (2012)

Hackbusch, W.: Truncation of tensors in the hierarchical format. same issue of SEMA (2018)

Khoromskij, B.: Tensors-structured numerical methods in scientific computing: survey on recent advances. Chemom. Intell. Lab. Syst. 110(1), 1–19 (2012)

Light, W.A., Cheney, E.W.: Approximation Theory in Tensor Product Spaces. Lect. Notes Math., 1169th edn. Springer, Berlin (1985)

Nouy, A.: Low-rank methods for high-dimensional approximation and model order reduction. In: Benner, P., Cohen, A., Ohlberger, M., Willcox, K. (eds.) Model Reduction and Approximation: Theory and Algorithms. SIAM, Philadelphia (2017)

Oseledets, I.V.: Tensor-train decomposition. SIAM J. Sci. Comput. 33, 2295–2317 (2011)

Vidal, G.: Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 91(14), 147902 (2003)