TITLE

DMRG Approach to Fast Linear Algebra in the TT-Format

AUTHOR(S)
Oseledets, Ivan
PUB. DATE
July 2011
SOURCE
Computational Methods in Applied Mathematics;2011, Vol. 11 Issue 3, p382
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, the concept of the DMRG minimization scheme is extended to several important operations in the TT-format, like the matrix-by-vector product and the conversion from the canonical format to the TT-format. Fast algorithms are implemented and a stabilization scheme based on randomization is proposed. The comparison with the direct method is performed on a sequence of matrices and vectors coming as approximate solutions of linear systems in the TT-format. A generated example is provided to show that randomization is really needed in some cases.
ACCESSION #
69616502

 

Related Articles

  • A Structured SVD-Like Decomposition. AGOUJIL, S.; BENTBIB, A. H.; Kanber, A. // WSEAS Transactions on Mathematics;Jul2012, Vol. 11 Issue 7, p627 

    We present in this paper a method that compute a symplectic SVD-like decomposition for a 2n-by-m rectangular real matrix. This decomposition focus mainly on numerical solution of some linear-quadratic optimal control theory and signal processing problems. In particular the resolution of...

  • Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains. Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph // PLoS Computational Biology;Mar2014, Vol. 10 Issue 3, p1 

    The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or...

  • Tensor Approximation Algorithm based on High Order Singular Value Decomposition. Yan-li Zhu; Jian-ping Wang; Xiao-juan Guo; Chang Liu // Journal of Convergence Information Technology;Aug2012, Vol. 7 Issue 15, p211 

    To solve some problems which JPEG compression obtains results of poor reconstruction quality and high computational complexity for image containing more high frequency information, a novel tensor approximation algorithm based on high order singular value decomposition has been proposed. The new...

  • Rank Properties of a Sequence of Block Bidiagonal Toeplitz Matrices. Kalogeropoulos, Grigoris I.; Karageorgos, Athanasios D.; Mitrouli, Marilena; Pantelous, Athanasios A. // Neural, Parallel & Scientific Computations;Mar2010, Vol. 18 Issue 1, p13 

    The article focuses on the algorithm for rank computation of Toeplitz matrices sequence. It mentions that the approach would serve as a basis for the numerical procedure that would compute the required nullity of a particular bidiagonal Toeplitz matrix sequence. It states that the computations...

  • A Low-Complexity Block Diagonalization Algorithm for MU-MIMO Two-Way Relay Systems with Complex Lattice Reduction. Xiao, Lin; Liu, Shengen; Yang, Dingcheng // International Journal of Distributed Sensor Networks;6/15/2015, Vol. 2015, p1 

    We design a scheme of precoding matrices for two-way multiuser relay systems, where a multiantenna relay station (RS) operating in an amplify-and-forward model simultaneously receives information from all multiple-antenna users. Considering the feasibility in mathematical analysis, users are...

  • The Study of FID Signal Processing Algorithm of Proton Magnetometer Based on SVD. Wang Hongliang; Dong Haobin; Hao Guocheng; Luo Yuansheng; Yu Zhihua // International Journal of Digital Content Technology & its Applic;Oct2012, Vol. 6 Issue 18, p139 

    In order to obtain useful signals and to improve the precision of frequency measurement of proton magnetometer free decay signal (FID signal), many methods had been taken to process the signal. However, many of them may be much better if they had considered the signal detection in a dynamic...

  • Uncovering Community Structures with Initialized Bayesian Nonnegative Matrix Factorization. Tang, Xianchao; Xu, Tao; Feng, Xia; Yang, Guoqing // PLoS ONE;Sep2014, Vol. 9 Issue 9, p1 

    Uncovering community structures is important for understanding networks. Currently, several nonnegative matrix factorization algorithms have been proposed for discovering community structure in complex networks. However, these algorithms exhibit some drawbacks, such as unstable results and...

  • Approximate Implicitization Using Linear Algebra. Barrowclough, Oliver J. D.; Dokken, Tor // Journal of Applied Mathematics;2012, p1 

    We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric...

  • Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm. Nakatani, Naoki; Chan, Garnet Kin-Lic // Journal of Chemical Physics;Apr2013, Vol. 138 Issue 13, p134113 

    We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics