메뉴 건너뛰기




Volumn 32, Issue 2, 2011, Pages 430-442

The best rank-one approximation ratio of a tensor space

Author keywords

Best rank one approximation ratio; Bounds; Tensors

Indexed keywords

APPROXIMATION RATIOS; BOUNDS; CONVERGENCE RATES; FINITE DIMENSIONAL; LOWER BOUNDS; TENSOR SPACES; THIRD ORDER; UPPER BOUND;

EID: 80051526441     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/100795802     Document Type: Article
Times cited : (78)

References (28)
  • 1
    • 78549238137 scopus 로고    scopus 로고
    • On the convergence of a greedy rank-one update algorithm for a class of linear systems
    • A. AMMAR, F. CHINESTA, AND A. X. FALCÓ, On the convergence of a greedy rank-one update algorithm for a class of linear systems, Arch. Comput. Methods Eng., 17(2010), pp. 473-486.
    • (2010) Arch. Comput. Methods Eng. , vol.17 , pp. 473-486
    • Ammar, A.1    Chinesta, F.2    Falcó, A.X.3
  • 2
    • 0032612381 scopus 로고    scopus 로고
    • High-order contrasts for independent component analysis
    • J. F. CARDOSO, High-order contrasts for independent component analysis, Neural Comput., 11(1999), pp. 157-192.
    • (1999) Neural Comput. , vol.11 , pp. 157-192
    • Cardoso, J.F.1
  • 3
    • 77953136528 scopus 로고    scopus 로고
    • A modified Newtons method for best rank-one approximation to tensors
    • J. CHANG, W. SUN, AND Y. CHEN, A modified Newtons method for best rank-one approximation to tensors, Appl. Math. Comput., 216(2010), pp. 1859-1867.
    • (2010) Appl. Math. Comput. , vol.216 , pp. 1859-1867
    • Chang, J.1    Sun, W.2    Chen, Y.3
  • 4
    • 0028416938 scopus 로고
    • Independent component analysis, a new concept?
    • P. COMON, Independent component analysis, a new concept?, Signal Processing, 36(1994), pp. 287-314.
    • (1994) Signal Processing , vol.36 , pp. 287-314
    • Comon, P.1
  • 5
    • 33751020575 scopus 로고    scopus 로고
    • A tensor product matrix approximation problem in quantum physics
    • DOI 10.1016/j.laa.2006.08.026, PII S0024379506004149
    • G. DAHL, J. M. LEINAAS, J. MYRHEIM, AND E. OVRUM, A tensor product matrix approximation problem in quantum physics, Linear Algebra Appl., 420(2007), pp. 711-725. (Pubitemid 44751797)
    • (2007) Linear Algebra and Its Applications , vol.420 , Issue.2-3 , pp. 711-725
    • Dahl, G.1    Leinaas, J.M.2    Myrheim, J.3    Ovrum, E.4
  • 8
    • 0039439070 scopus 로고    scopus 로고
    • Some remarks on greedy algorithm
    • R. DEVORE AND V. TELMYAKOV, Some remarks on greedy algorithm, Adv. Comput. Math., 5(1996), pp. 173-187.
    • (1996) Adv. Comput. Math. , vol.5 , pp. 173-187
    • Devore, R.1    Telmyakov, V.2
  • 9
    • 78650698308 scopus 로고    scopus 로고
    • A proper generalized decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach
    • A. FALÓ AND A. NOUY, A proper generalized decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach, J. Math. Anal. Appl., 376(2011), pp. 469-480.
    • (2011) J. Math. Anal. Appl. , vol.376 , pp. 469-480
    • Faló, A.1    Nouy, A.2
  • 10
    • 58149501168 scopus 로고    scopus 로고
    • Tensor displacement structures and polyspectral matching
    • T. Kailath and A. H. Sayed, eds., SIAM, Philadeliphia
    • V. S. GRIGORASCU AND P. A. REGALIA, Tensor displacement structures and polyspectral matching, in Fast Reliable Algorithms for Structured Matrices, T. Kailath and A. H. Sayed, eds., SIAM, Philadeliphia, 1999.
    • (1999) Fast Reliable Algorithms for Structured Matrices
    • Grigorascu, V.S.1    Regalia, P.A.2
  • 11
    • 65649110856 scopus 로고    scopus 로고
    • Conditions for strong ellipticity of anisotropic elastic materials
    • D. HAN, H. H. DAI, AND L. QI, Conditions for strong ellipticity of anisotropic elastic materials, J. Elasticity, 97(2009), pp. 1-13.
    • (2009) J. Elasticity , vol.97 , pp. 1-13
    • Han, D.1    Dai, H.H.2    Qi, L.3
  • 12
    • 0036018642 scopus 로고    scopus 로고
    • On the best rank-1 approximation of higher-order supersymmetric tensors
    • E. KOFIDIS AND P. A. REGALIA, On the best rank-1 approximation of higher-order supersymmetric tensors, SIAM J. Matrix Anal. Appl., 23(2002), pp. 863-884.
    • (2002) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 863-884
    • Kofidis, E.1    Regalia, P.A.2
  • 13
    • 0031256756 scopus 로고    scopus 로고
    • Une décomposition en valeurs singulières d'un élément d'un produit tensoriel de k espaces de Hilbert séparables
    • D. LEIBOVICI AND H. EL MAÂCHE, Une decomposition en valeurs singuliers d'un element d'un produit tensoriel de k-espaces de Hilbert separables, C. R. Math. Acad. Sci. Paris, 325 (1997) pp. 779-782. (Pubitemid 127165084)
    • (1997) Comptes Rendus de l'Academie des Sciences - Series I: Mathematics , vol.325 , Issue.7 , pp. 779-782
    • Leibovici, D.1    El Maache, H.2
  • 14
    • 33846606151 scopus 로고    scopus 로고
    • Singular values and eigenvalues of tensors: A variational approach
    • DOI 10.1109/CAMAP.2005.1574201, 1574201, IEEE CAMSAP 2005 - First International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
    • L.-H. LIM, Singular values and eigenvalues of tensors: A variational approach, in Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP'05), 1(2005), pp. 129-132. (Pubitemid 46170894)
    • (2005) IEEE CAMSAP 2005 - First International Workshop on Computational Advances in Multi-Sensor Adaptive Processing , vol.2005 , pp. 129-132
    • Lim, L.-H.1
  • 15
    • 34548409985 scopus 로고    scopus 로고
    • On the best rank-1 approximation to higher-order symmetric tensors
    • DOI 10.1016/j.mcm.2007.01.008, PII S089571770700060X
    • G. NI AND Y. WANG, On the best rank-1 approximation to higher-order symmetric tensors, Math. Comput. Model., 46(2007), pp. 1345-1352. (Pubitemid 47362621)
    • (2007) Mathematical and Computer Modelling , vol.46 , Issue.9-10 , pp. 1345-1352
    • Ni, G.1    Wang, Y.2
  • 16
    • 73249147288 scopus 로고    scopus 로고
    • Bi-quadratic optimization over unit spheres and semidefinite programming relaxations
    • C. LING, J. NIE, L. QI, AND Y. YE, Bi-quadratic optimization over unit spheres and semidefinite programming relaxations, SIAM J. Optim., 20(2009), pp. 1286-1310.
    • (2009) SIAM J. Optim. , vol.20 , pp. 1286-1310
    • Ling, C.1    Nie, J.2    Qi, L.3    Ye, Y.4
  • 19
    • 27744582534 scopus 로고    scopus 로고
    • Eigenvalues of a real supersymmetric tensor
    • DOI 10.1016/j.jsc.2005.05.007, PII S0747717105000817
    • L. QI, Eigenvalues of a real supersymmetric tensor, J. Symbolic Comput., 40(2005), pp. 1302-1324. (Pubitemid 41600816)
    • (2005) Journal of Symbolic Computation , vol.40 , Issue.6 , pp. 1302-1324
    • Qi, L.1
  • 20
    • 63949087720 scopus 로고    scopus 로고
    • Conditions for strong ellipticity and M-eigenvalues
    • L. QI, H. H. DAI, AND D. HAN, Conditions for strong ellipticity and M-eigenvalues, Front. Math. China, 4(2009), pp. 349-364.
    • (2009) Front. Math. China , vol.4 , pp. 349-364
    • Qi, L.1    Dai, H.H.2    Han, D.3
  • 21
    • 58149504770 scopus 로고    scopus 로고
    • Z-eigenvalue methods for a global optimization polynomial optimization problem
    • L. QI, F. WANG, AND Y. WANG, Z-eigenvalue methods for a global optimization polynomial optimization problem, Math. Program., 118(2009), pp. 301-306.
    • (2009) Math. Program. , vol.118 , pp. 301-306
    • Qi, L.1    Wang, F.2    Wang, Y.3
  • 22
    • 81155134640 scopus 로고    scopus 로고
    • Deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems
    • to appear
    • A. M.-C. SO, Deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems, Math. Program., to appear.
    • Math. Program.
    • So, A.M.-C.1
  • 23
    • 54949114684 scopus 로고    scopus 로고
    • Estimating crossing fibers: A tensor decomposition approach
    • T. SCHULTZ AND H.-P. SEIDEL, Estimating crossing fibers: A tensor decomposition approach, IEEE Trans. Vis. Comput. Graph., 14(2008), pp. 1635-1642.
    • (2008) IEEE Trans. Vis. Comput. Graph. , vol.14 , pp. 1635-1642
    • Schultz, T.1    Seidel, H.-P.2
  • 24
    • 34547842082 scopus 로고    scopus 로고
    • On the successive supersymmetric rank-1 decomposition of higher order supersymmetric tensors
    • Y. WANG AND L. QI, On the successive supersymmetric rank-1 decomposition of higher order supersymmetric tensors, Numer. Linear Algebra Appl., 14(2007), pp. 503-519.
    • (2007) Numer. Linear Algebra Appl. , vol.14 , pp. 503-519
    • Wang, Y.1    Qi, L.2
  • 25
    • 67650553280 scopus 로고    scopus 로고
    • A practical method for computing the largest M-eigenvalue of a fourthorder partially symmetric tensor
    • Y. WANG, L. QI, AND X. ZHANG, A practical method for computing the largest M-eigenvalue of a fourthorder partially symmetric tensor, Numer. Linear Algebra Appl., 16(2009), pp. 589-601.
    • (2009) Numer. Linear Algebra Appl. , vol.16 , pp. 589-601
    • Wang, Y.1    Qi, L.2    Zhang, X.3
  • 26
    • 0036056838 scopus 로고    scopus 로고
    • Rank-1 approximation of higher-order tensors
    • T. ZHANG AND G. H. GOLUB, Rank-1 approximation of higher-order tensors, SIAM J. Matrix Anal. Appl., 23(2001), pp. 534-550.
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 534-550
    • Zhang, T.1    Golub, G.H.2
  • 27
    • 79951555291 scopus 로고    scopus 로고
    • Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints
    • X. ZHANG, C. LING, AND L. QI, Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints, J. Global Optim., 49(2011), pp. 293-311.
    • (2011) J. Global Optim. , vol.49 , pp. 293-311
    • Zhang, X.1    Ling, C.2    Qi, L.3
  • 28
    • 80051481667 scopus 로고    scopus 로고
    • The cubic spherical optimization problem
    • to appear
    • X. ZHANG, L. QI, AND Y. YE, The cubic spherical optimization problem, Math. Comp., to appear.
    • Math. Comp.
    • Zhang, X.1    Qi, L.2    Ye, Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.