메뉴 건너뛰기




Volumn 13, Issue 2, 2005, Pages 119-156

Hierarchical Kronecker tensor-product approximations

Author keywords

BEM; Hierarchical matrices; Integral equations; Kronecker products; Low rank matrices; Multi dimensional matrices; Tensors

Indexed keywords

BOUNDARY ELEMENT METHOD; COMPUTATIONAL METHODS; HIERARCHICAL SYSTEMS; INTEGRAL EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS; MATRIX ALGEBRA; TENSORS;

EID: 21244436795     PISSN: 15702820     EISSN: None     Source Type: Journal    
DOI: 10.1163/1569395054012767     Document Type: Article
Times cited : (96)

References (39)
  • 1
    • 5844381624 scopus 로고    scopus 로고
    • Approximation of boundary element matrices
    • M. Bebendorf, Approximation of boundary element matrices. Numer. Math. (2000) 86, 565-589.
    • (2000) Numer. Math. , vol.86 , pp. 565-589
    • Bebendorf, M.1
  • 3
    • 0036679114 scopus 로고    scopus 로고
    • Numerical operator calculus in higher dimensions
    • G. Beylkin and M. M. Mohlenkamp, Numerical operator calculus in higher dimensions. Proc. Natl. Acad. Sci. USA (2002) 99, 10246-10251.
    • (2002) Proc. Natl. Acad. Sci. USA , vol.99 , pp. 10246-10251
    • Beylkin, G.1    Mohlenkamp, M.M.2
  • 4
    • 21244487234 scopus 로고    scopus 로고
    • Preprint No. 5, Max-Planck-Institut für Mathematik, Leipzig
    • 2-matrices. Preprint No. 5, Max-Planck-Institut für Mathematik, Leipzig, 2003.
    • (2003) 2-matrices
    • Börm, S.1    Hackbusch, W.2
  • 5
    • 0026413037 scopus 로고
    • Multilevel computations of integral transforms and particle interactions with oscillatory kernels
    • A. Brandt, Multilevel computations of integral transforms and particle interactions with oscillatory kernels. Comp. Phys. Comm. (1991) 65, 24-38.
    • (1991) Comp. Phys. Comm. , vol.65 , pp. 24-38
    • Brandt, A.1
  • 7
    • 2942606241 scopus 로고    scopus 로고
    • Combining Kronecker product approximation with discrete wavelet transforms to solve dense, function-related systems
    • J.M. Ford and E. E. Tyrtyshnikov, Combining Kronecker product approximation with discrete wavelet transforms to solve dense, function-related systems. SIAM J. Sci. Comp. (2003) 25, No. 3, 961-981.
    • (2003) SIAM J. Sci. Comp. , vol.25 , Issue.3 , pp. 961-981
    • Ford, J.M.1    Tyrtyshnikov, E.E.2
  • 8
    • 0036022621 scopus 로고    scopus 로고
    • ℋ-Matrix approximation for the operator exponential with applications
    • I. P. Gavrilyuk, W. Hackbusch, and B. N. Khoromskij, ℋ-Matrix approximation for the operator exponential with applications. Numer. Math. (2002) 92, 83-111.
    • (2002) Numer. Math. , vol.92 , pp. 83-111
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 9
    • 0034936175 scopus 로고    scopus 로고
    • ℋ-Matrix approximation for elliptic solution operators in cylinder domains
    • I. P. Gavrilyuk, W. Hackbusch, and B. N. Khoromskij, ℋ-Matrix approximation for elliptic solution operators in cylinder domains. East-West J. Numer. Math. (2001) 9, No. 1, 25-59.
    • (2001) East-West J. Numer. Math. , vol.9 , Issue.1 , pp. 25-59
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 10
    • 2942644816 scopus 로고    scopus 로고
    • Data-sparse approximation to operator-valued functions of elliptic operators
    • I. P. Gavrilyuk, W. Hackbusch, and B. N. Khoromskij, Data-sparse approximation to operator-valued functions of elliptic operators. Math. Comp. (2004) 73, No. 247, 1297-1324.
    • (2004) Math. Comp. , vol.73 , Issue.247 , pp. 1297-1324
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 11
    • 14944359407 scopus 로고    scopus 로고
    • Data-sparse approximation to a class of operator-valued functions
    • I. P. Gavrilyuk, W. Hackbusch, and B. N. Khoromskij, Data-sparse approximation to a class of operator-valued functions. Math. Comp. (2005) 74, 681-708.
    • (2005) Math. Comp. , vol.74 , pp. 681-708
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 13
    • 0037790752 scopus 로고    scopus 로고
    • The maximal-volume concept in approximation by low-rank matrices
    • S. A. Goreinov, E. E. Tyrtyshnikov, The maximal-volume concept in approximation by low-rank matrices. Contemporary Mathematics (2001) 208, 47-51.
    • (2001) Contemporary Mathematics , vol.208 , pp. 47-51
    • Goreinov, S.A.1    Tyrtyshnikov, E.E.2
  • 16
    • 3042756404 scopus 로고    scopus 로고
    • Existence and computation of a low Kronecker-rank approximant to the solution of a tensor system with tensor right-hand side
    • L. Grasedyck, Existence and computation of a low Kronecker-rank approximant to the solution of a tensor system with tensor right-hand side. Computing (2004) 72, 247-265.
    • (2004) Computing , vol.72 , pp. 247-265
    • Grasedyck, L.1
  • 17
    • 0141829814 scopus 로고    scopus 로고
    • Construction and arithmetics of ℋ-matrices
    • L. Grasedyck and W. Hackbusch, Construction and arithmetics of ℋ-matrices. Computing (2003) 70, 295-334.
    • (2003) Computing , vol.70 , pp. 295-334
    • Grasedyck, L.1    Hackbusch, W.2
  • 18
    • 0032637646 scopus 로고    scopus 로고
    • A sparse matrix arithmetic based on ℋ-matrices. I. Introduction to ℋ-matrices
    • W. Hackbusch, A sparse matrix arithmetic based on ℋ-matrices. I. Introduction to ℋ-matrices. Computing (1999) 62, 89-108.
    • (1999) Computing , vol.62 , pp. 89-108
    • Hackbusch, W.1
  • 19
    • 0002133258 scopus 로고    scopus 로고
    • A sparse ℋ-matrix arithmetic. II. Application to multi-dimensional problems
    • W. Hackbusch and B. N. Khoromskij, A sparse ℋ-matrix arithmetic. II. Application to multi-dimensional problems. Computing (2000) 64, 21-47.
    • (2000) Computing , vol.64 , pp. 21-47
    • Hackbusch, W.1    Khoromskij, B.N.2
  • 20
    • 0034509772 scopus 로고    scopus 로고
    • A sparse ℋ-matrix arithmetic: General complexity estimates
    • W. Hackbusch and B. N. Khoromskij, A sparse ℋ-matrix arithmetic: General complexity estimates. J. Comp. Appl. Math. (2000) 125, 479-501.
    • (2000) J. Comp. Appl. Math. , vol.125 , pp. 479-501
    • Hackbusch, W.1    Khoromskij, B.N.2
  • 21
    • 0013004192 scopus 로고    scopus 로고
    • Towards ℋ-matrix approximation of the linear complexity
    • Birkhäuser Verlag
    • W.Hackbusch and B.N.Khoromskij, Towards ℋ-matrix approximation of the linear complexity. In: Operator Theory: Advances and Applications, Birkhäuser Verlag, 2001, Vol. 121, pp. 194-220.
    • (2001) Operator Theory: Advances and Applications , vol.121 , pp. 194-220
    • Hackbusch, W.1    Khoromskij, B.N.2
  • 24
    • 10644283019 scopus 로고    scopus 로고
    • Hierarchical matrices based on a weak admissibility criterion
    • W. Hackbusch, B. N. Khoromskij, and R. Kriemann, Hierarchical matrices based on a weak admissibility criterion. Computing (2004) 73, 207-243.
    • (2004) Computing , vol.73 , pp. 207-243
    • Hackbusch, W.1    Khoromskij, B.N.2    Kriemann, R.3
  • 27
    • 0001617415 scopus 로고
    • On the fast matrix multiplication in the boundary elements method by panel clustering
    • W. Hackbusch and Z.P. Nowak, On the fast matrix multiplication in the boundary elements method by panel clustering. Numer. Math.(1989) 54, 463-491.
    • (1989) Numer. Math. , vol.54 , pp. 463-491
    • Hackbusch, W.1    Nowak, Z.P.2
  • 28
    • 0036391742 scopus 로고    scopus 로고
    • Application of 3-way decomposition for matrix compression
    • I. Ibraghimov, Application of 3-way decomposition for matrix compression. Numer. Linear Algebra Appl. (2002) 9, 551-565.
    • (2002) Numer. Linear Algebra Appl. , vol.9 , pp. 551-565
    • Ibraghimov, I.1
  • 31
    • 46549096170 scopus 로고
    • Rapid solution of integral equations of classical potential theory
    • V. Rokhlin, Rapid solution of integral equations of classical potential theory. J. Comp. Phys. (1985) 60, 187-207.
    • (1985) J. Comp. Phys. , vol.60 , pp. 187-207
    • Rokhlin, V.1
  • 33
    • 0035359436 scopus 로고    scopus 로고
    • A matrix version of the fast multipole method
    • X. Sun, N. P. Pitsianis, A matrix version of the fast multipole method. SIAM Review (2001) 43, 289-300.
    • (2001) SIAM Review , vol.43 , pp. 289-300
    • Sun, X.1    Pitsianis, N.P.2
  • 34
    • 84944459960 scopus 로고    scopus 로고
    • Mosaic ranks and skeletons
    • (Eds. L. Vulkov, J. Wasniewski, and P. Yalamov), Lecture Notes in Computer Science. Springer-Verlag
    • E.E.Tyrtyshnikov, Mosaic ranks and skeletons. In: Numerical Analysis and its Applications (Eds. L. Vulkov, J. Wasniewski, and P. Yalamov), Lecture Notes in Computer Science, Vol. 1196. Springer-Verlag, 1996, pp. 505-516.
    • (1996) Numerical Analysis and Its Applications , vol.1196 , pp. 505-516
    • Tyrtyshnikov, E.E.1
  • 35
    • 0029692981 scopus 로고    scopus 로고
    • Mosaic-skeleton approximations
    • E. E. Tyrtyshnikov, Mosaic-skeleton approximations. Calcolo (1996) 33, 47-57.
    • (1996) Calcolo , vol.33 , pp. 47-57
    • Tyrtyshnikov, E.E.1
  • 36
    • 0038805356 scopus 로고    scopus 로고
    • Incomplete cross approximation in the mosaic-skeleton method
    • E. E. Tyrtyshnikov, Incomplete cross approximation in the mosaic-skeleton method. Computing (2000) 64, 367-380.
    • (2000) Computing , vol.64 , pp. 367-380
    • Tyrtyshnikov, E.E.1
  • 37
    • 0742320626 scopus 로고    scopus 로고
    • Kronecker-product approximations for some function-related matrices
    • E. E. Tyrtyshnikov, Kronecker-product approximations for some function-related matrices. Linear Algebra Appl. (2004) 379, 423-437.
    • (2004) Linear Algebra Appl. , vol.379 , pp. 423-437
    • Tyrtyshnikov, E.E.1
  • 38
    • 17144425622 scopus 로고    scopus 로고
    • Tensor approximations of matrices associated with asymptotically smooth functions
    • E. E. Tyrtyshnikov, Tensor approximations of matrices associated with asymptotically smooth functions. Sbor. Math. (2003) 194, No. 6, 147-160.
    • (2003) Sbor. Math. , vol.194 , Issue.6 , pp. 147-160
    • Tyrtyshnikov, E.E.1
  • 39
    • 0002203498 scopus 로고
    • Approximation with Kronecker products
    • Kluwer, Dordrecht
    • C. F. Van Loan and N. P. Pitsianis, Approximation with Kronecker products. NATO Adv. Sci. Ser. E Appl. Sci., Vol. 232, Kluwer, Dordrecht, 1993, pp. 293-314.
    • (1993) NATO Adv. Sci. Ser. E Appl. Sci. , vol.232 , pp. 293-314
    • Van Loan, C.F.1    Pitsianis, N.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.