Distributed hierarchical SVD in the Hierarchical Tucker format

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

htucker – A Matlab toolbox for tensors in hierarchical Tucker format

The hierarchical Tucker format is a storage-efficient scheme to approximate and represent tensors of possibly high order. This paper presents a Matlab toolbox, along with the underlying methodology and algorithms, which provides a convenient way to work with this format. The toolbox not only allows for the efficient storage and manipulation of tensors but also offers a set of tools for the deve...

متن کامل

Black Box Approximation of Tensors in Hierarchical Tucker Format

We derive and analyse a scheme for the approximation of order d tensors A ∈ R n×···×n in the hierarchical (H-) Tucker format, a dimension-multilevel variant of the Tucker format and strongly related to the TT format. For a fixed rank parameter k, the storage complexity of a tensor in H-Tucker format is O(dk 3 + dnk) and we present a (heuristic) algorithm that finds an approximation to a tensor ...

متن کامل

Polynomial Approximation in Hierarchical Tucker Format by Vector–Tensorization

We analyze and characterize the possibility to represent or approximate tensors that stem from a tensorization of vectors, matrices, or tensors by low (hierarchical) rank. Our main result is that for vectors that stem from the evaluation of a polynomial f of degree p on an equispaced grid, the (hierarchical) rank is bounded by 1 + p. This is not true for the canonical rank, and we prove this by...

متن کامل

Sampling Rules for Tensor Reconstruction in Hierarchical Tucker Format

The subject of this article is the development of an algorithm that reconstructs a high-dimensional tensor by a hierarchical (H-) Tucker tensor with the help of a non-adaptive sampling rule. This sampling rule supports our approximation scheme coming from the matrix cross approximation and guarantees that we can build a tensor A H in the desired format from only a few entries of the original te...

متن کامل

On the approximation of high-dimensional differential equations in the hierarchical Tucker format

The hierarchical Tucker format is a way to decompose a high-dimensional tensor recursively into sums of products of lower-dimensional tensors. The number of degrees of freedom in such a representation is typically many orders of magnitude lower than the number of entries of the original tensor. This makes the hierarchical Tucker format a promising approach to solve ordinary differential equatio...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Numerical Linear Algebra with Applications

سال: 2018

ISSN: 1070-5325

DOI: 10.1002/nla.2174