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An Analysis of the Vector Decomposition Problem [chapter]

Steven D. Galbraith, Eric R. Verheul
Public Key Cryptography – PKC 2008  
The vector decomposition problem (VDP) has been proposed as a computational problem on which to base the security of public key cryptosystems.  ...  We give a generalisation and simplification of the results of Yoshida on the VDP.  ...  Acknowledgements We thank Iwan Duursma, Seung-Kook Park, Maura Paterson and a number of anonymous referees for helpful comments on a much earlier draft of the paper.  ... 
doi:10.1007/978-3-540-78440-1_18 dblp:conf/pkc/GalbraithV08 fatcat:zeasijzfz5ayzhtb3ae2jadyja

Analysis-Based Nonlocal-Approximate Sparsity Representation in Image Processing

Xiaowei He, Li Zhang, Jiping Xiong
2016 International Journal of Signal Processing, Image Processing and Pattern Recognition  
we proposed a nonlocal-approximate sparsity regularizer in analysis domains by minimizing the sum of the 2 l norms of those vectors with the same nonzero pattern like signal vectors.  ...  In this paper, based on a simple observation that the non-zero entries of the sparsity vector in various image analysis domains should be also approximate when the relevant signal values are proximate,  ...  The authors would like to thank three anonymous reviewers for their valuable comments and constructive suggestions.  ... 
doi:10.14257/ijsip.2016.9.9.08 fatcat:kt5to4g2rnaihnyfwxn2puv3si

Tensorial resolution: A direct trilinear decomposition

Eugenio Sanchez, Bruce R. Kowalski
1990 Journal of Chemometrics  
APPENDIX III: DIRECT TRILINEAR DECOMPOSITION ALGORITHM The direct solution of the trilinear decomposition problem by reduction to an eigenvalue—eigenvector problem can be outlined in three steps: (1) Tucker  ...  Unfortunately, there are an infinite number of possible decompositions of R, and no unambiguous solution of the problem is possible without further information.  ... 
doi:10.1002/cem.1180040105 fatcat:x6h32x6jfvezfazgpbjfdvvgaq

Original Derivation of the Modal Decomposition Analysis for Solving Mixed Boundary-Initial Value Problems

A. Moura
2004 International Journal of Acoustics and Vibration  
This paper using an original approach introduces the well-known modal decomposition analysis for solving mixed boundary-initial value problems.  ...  These particular problems have been studied by means of the so-called modal decomposition analysis 1 by mechanical engineers since the fifties 2 .  ... 
doi:10.20855/ijav.2004.9.3164 fatcat:qfjpqmbvvbdvtouc7daetnklnm

Large-scale smooth plastic topology optimization using domain decomposition

Mohamed Fourati, Zied Kammoun, Jamel Neji, Hichem Smaoui
2021 Comptes Rendus Mecanique  
It takes advantage of the favorable features of the integrated limit analysis and design formulation of the smooth topology design problem.  ...  The integrated approach preserves the mathematical structure and properties of the underlying static, lower bound problem of limit analysis.  ...  The displacements or velocities can be interpreted as dual variables in the dual problem, which is an expression of the kinematic (upper bound) problem of limit analysis.  ... 
doi:10.5802/crmeca.88 fatcat:ufm4zpiqpjhs7oeqcibn5z6ema

Frame-based Approach for Sparse Representation of Signal Decomposition and Reconstruction [article]

Wen-Liang Hwang
2017 arXiv   pre-print
A celebrated result indicates that if a synthesis frame is chosen for reconstruction, then its canonical dual frame is the analysis frame that performs decomposition, yielding coefficients that minimizes  ...  However, we present some conditions on a dual frame so that the minimizer of the l1-norm can be derived from the coefficients of the dual frame.  ...  The composition of the reconstruction operation after the decomposition operation must be an identity operation.  ... 
arXiv:1603.09492v2 fatcat:pg4qc6nxkngm3kbwvt7g6k5yma

Fast computation of minimal elementary decompositions of metabolic flux vectors

Raphael M. Jungers, Francisca Zamorano, Vincent D. Blondel, Alain Vande Wouwer, Georges Bastin
2011 Automatica  
Fast computation of minimal elementary decompositions of metabolic flux vectors. a b s t r a c t The concept of elementary flux vector is valuable in a number of applications of metabolic engineering.  ...  For instance, in metabolic flux analysis, each admissible flux vector can be expressed as a non-negative linear combination of a small number of elementary flux vectors.  ...  A matlab implementation of our algorithms is available on  ... 
doi:10.1016/j.automatica.2011.01.011 fatcat:qp22v3cyfngslfh4pedcvqftr4

Rapid singular value decomposition for time-domain analysis of magnetic resonance signals by use of the lanczos algorithm

Glenn L Millhauser, Alison A Carter, David J Schneider, Jack H Freed, Robert E Oswald
1989 Journal of Magnetic Resonance (1969)  
Time-series analysis has become an integral part of signal interpretation in magnetic resonance and other experiments.  ...  The minimal goal of time-series analysis is to separate signal from noise.  ...  The SVD problem can be reduced to an eigenelement problem by construction of the real symmetric matrix 0- 0 T, = 0 P3 0 a** 0 [51 . . . 0 0 0 *** ij -0 0 0 *'* @j O- and{ul,u2,...  ... 
doi:10.1016/0022-2364(89)90175-3 fatcat:llgkylymeba6rialhdjtt67tka

Book announcements

1991 Discrete Applied Mathematics  
The MSCCC queueing discipline). Reversible queueing networks. Applications of queueing network models (Queueing network models of computer systems.  ...  Queueing network model of a distributed computer system. Queueing network models of communication networks. Queueing model of a network of workstations. Queueing model of a circuit-switched network.  ...  Properties of the A matrix. Representation of a nonbasic vector in terms of the basic vectors. The simplex method for network flow problems. An example of the network simplex method.  ... 
doi:10.1016/0166-218x(91)90006-i fatcat:gwvpijrtynhrdgyral35zuaeay

Page 7034 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
These techniques are justified by an analysis of the regularized solutions based on the singular value decomposition and the generalized singular value decomposition.  ...  The ULV decomposition (ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD).  ... 

Smooth orthogonal decomposition for modal analysis of randomly excited systems

U. Farooq, B.F. Feeny
2008 Journal of Sound and Vibration  
Using output response ensembles only, the generalized eigenvalue problem is formed to estimate eigen frequencies and modal vectors for an eight-degree-of-freedom lightly damped vibratory system.  ...  This work shows that under certain conditions, the smooth orthogonal decomposition eigenvalue problem formulated from white noise induced response data can be tied to the unforced structural eigenvalue  ...  For visualization, the modal vectors from smooth orthogonal decomposition and the structural eigenvalue problem are compared in Fig. 2 .  ... 
doi:10.1016/j.jsv.2008.02.052 fatcat:hs3fiv7bera4zimsajeayd2voe

Page 966 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
The idea of considering ab- stract vector variables came from an attempt to formulate Clifford algebra and analysis independent of the choice of the dimension m, independent of coordinates and bases and  ...  [Sommen, Franciscus] (B-GHNT-AN; Ghent) Clifford analysis on the level of abstract vector variables. (English summary) Clifford analysis and its applications (Prague, 2000), 303-322, NATO Sci. Ser.  ... 

Two alternative ways for solving the coordination problem in multilevel optimization

J. Sobieszczanski-Sobieski
1993 Structural Optimization  
NE(13) System Analysis, designated SA, is regarded as a black box that converts an input vector {,5'I} of length NS[ into an output vector {SO} of length NSO.  ...  The above approach suggests decomposition of the framework analysis into the assembled framework analysis (system level analysis) and the beam analyses (subsystem level analyses).  ...  The old and the new formulations are presentedin detail,illustrated by an exampleof a structuraloptimization.  ... 
doi:10.1007/bf01743377 fatcat:mj6l6jdv5rfb5p6nn6vvl4uqmq

Stochastic and Deterministic Tensorization for Blind Signal Separation [chapter]

Otto Debals, Lieven De Lathauwer
2015 Lecture Notes in Computer Science  
The source signals, mixing vectors and sensor signals are contained in S, M and X, respectively. One can see that the problem consists of a matrix factorization of X.  ...  Introduction Given a mixture of some source signals, the Blind Signal Separation (BSS) problem consists of the identification of both the mixing matrix and the original sources.  ...  The source signals, mixing vectors and sensor signals are contained in S, M and X, respectively. One can see that the problem consists of a matrix factorization of X.  ... 
doi:10.1007/978-3-319-22482-4_1 fatcat:ko7cqjsakzapbh3jpedzfunzxm

ECG Energy Change Study Based on Variational Mode Decomposition

Kai Dong, Lin Sun, Hongjun Xiong, Wenbo Wang
2020 American Journal of Biochemistry and Biotechnology  
Then, the energy vectors of ECG signals are obtained by calculating the energy of each IMTF and a comparative analysis of energy vectors is conducted between healthy people and three kinds of heart disease  ...  thus very suitable for the analysis of nonlinear and non-stationary Electrocardiogram (ECG) signal.  ...  VMD Energy Vector Analysis of ECG VMD Decomposition of ECG We selected the healthy people normal sinus rhythm database (nsrdb) of MIT-BIH as experimental data for VMD decomposition.  ... 
doi:10.3844/ajbbsp.2020.103.111 fatcat:6xd45wgjebfmhmxhks2bbyc2ru
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