Abstract In this article, we analyze tensor approximation schemes for continuous functions. We assume that the function to be approximated lies in an isotropic Sobolev space and discuss cost when approximating analogue of Tucker format or train format. especially show both approximations are dimension-robust under consideration provides appropriate dimension weights.

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discu...

Tensor-based methods are receiving a growing interest in scienti c computing for the numerical solution of problems de ned in high dimensional tensor product spaces. A family of methods called Proper Generalized Decompositions methods have been recently introduced for the a priori construction of tensor approximations of the solution of such problems. In this paper, we give a mathematical analy...

We propose a Bayesian approach to regression with a scalar response on vector and tensor covariates. Vectorization of the tensor prior to analysis fails to exploit the structure, often leading to poor estimation and predictive performance. We introduce a novel class of multiway shrinkage priors for tensor coefficients in the regression setting and present posterior consistency results under mil...

polycyclic aromatic hydrocarbons (pahs) are a class of compounds consisting of more than twobenzene rings fused in a linear, angular, or clustered arrangement and do not contain hetero atomsor carry subsistent. pahs originate from various sources. they are primarily formed byincomplete combustion of carbon-containing fuels such as wood, coal, diesel, fat, or tobacco. thepresent study reports an...