Hdl Handle:
http://hdl.handle.net/10034/123074
Title:
Tensor decomposition and its applications
Authors:
Tock, Daniel
Abstract:
This dissertation reviews classical vector - tensor analysis, building up to the necessary techniques required to decompose a tensor into a tensor train and to reconstruct it back into the original tensor with minimal error. The tensor train decomposition decomposes a tensor of dimensionality d into a train of d third order tensors, whose sizes are dependent upon the rank and chosen error bound. I will be reviewing the required operations of matricization, tensor - matrix, vector and tensor multiplication to be able to compute this decomposition. I then move onto analysing the tensor train decomposition by ap-plying it to different types of tensor, of differing dimensionality with a variety of accuracy bounds to investigate their influence on the time taken to complete the decomposition and the final absolute error. Finally I explore a method to compute a d-dimensional integration from the tensor train, which will allow larger tensors to be integrated with the memory required dramatically reduced after the tensor is decomposed. I will be applying this technique to two tensors with different ranks and compare the efficiency and accuracy of integrating directly from the tensor to that of the tensor train decomposition.
Advisors:
Roberts, Jason
Publisher:
University of Chester
Issue Date:
Sep-2010
URI:
http://hdl.handle.net/10034/123074
Type:
Thesis or dissertation
Language:
en
Appears in Collections:
MPhil / PhD Theses and Masters Dissertations

Full metadata record

DC FieldValueLanguage
dc.contributor.advisorRoberts, Jasonen
dc.contributor.authorTock, Danielen
dc.date.accessioned2011-02-28T13:12:44Z-
dc.date.available2011-02-28T13:12:44Z-
dc.date.issued2010-09-
dc.identifier.urihttp://hdl.handle.net/10034/123074-
dc.description.abstractThis dissertation reviews classical vector - tensor analysis, building up to the necessary techniques required to decompose a tensor into a tensor train and to reconstruct it back into the original tensor with minimal error. The tensor train decomposition decomposes a tensor of dimensionality d into a train of d third order tensors, whose sizes are dependent upon the rank and chosen error bound. I will be reviewing the required operations of matricization, tensor - matrix, vector and tensor multiplication to be able to compute this decomposition. I then move onto analysing the tensor train decomposition by ap-plying it to different types of tensor, of differing dimensionality with a variety of accuracy bounds to investigate their influence on the time taken to complete the decomposition and the final absolute error. Finally I explore a method to compute a d-dimensional integration from the tensor train, which will allow larger tensors to be integrated with the memory required dramatically reduced after the tensor is decomposed. I will be applying this technique to two tensors with different ranks and compare the efficiency and accuracy of integrating directly from the tensor to that of the tensor train decomposition.en
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.subjectclassical vector - tensor analysisen
dc.titleTensor decomposition and its applicationsen
dc.typeThesis or dissertationen
dc.type.qualificationnameMScen
dc.type.qualificationlevelMasters Degreeen
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