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Volumn 48, Issue 1, 2000, Pages 35-66

Optimal multilevel matrix algebra operators

Author keywords

Korovkin theorem; Masking operators; Matrix vector spaces and matrix algebras; Toeplitz matrices

Indexed keywords


EID: 0002839615     PISSN: 03081087     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (23)

References (43)
  • 1
    • 0021422840 scopus 로고
    • Parallel solution of certain Toeplitz linear systems
    • Bini, D. (1984). "Parallel solution of certain Toeplitz linear systems", SIAM J. Comput., 13, 268-276.
    • (1984) SIAM J. Comput. , vol.13 , pp. 268-276
    • Bini, D.1
  • 2
    • 0002887353 scopus 로고
    • Spectral and computational properties of band symmetric Toeplitz matrices
    • Bini, D. and Capovani, M. (1983). "Spectral and computational properties of band symmetric Toeplitz matrices", Linear Algebra Appl., 52/53, 99-126.
    • (1983) Linear Algebra Appl. , vol.52-53 , pp. 99-126
    • Bini, D.1    Capovani, M.2
  • 3
    • 21144460588 scopus 로고
    • On a matrix algebra related to the discrete Hartley transform
    • Bini, D. and Favati, P. (1993). "On a matrix algebra related to the discrete Hartley transform", SIAM J. Matrix Anal. Appl., 14, 500-507.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 500-507
    • Bini, D.1    Favati, P.2
  • 5
    • 0002636630 scopus 로고
    • Circulant preconditioned for elliptic problems
    • Chan, R. H. and Chan, T. F. (1992). "Circulant preconditioned for elliptic problems", J. Numer. Linear Algebra Appl., 1, 77-101.
    • (1992) J. Numer. Linear Algebra Appl. , vol.1 , pp. 77-101
    • Chan, R.H.1    Chan, T.F.2
  • 6
    • 26844496501 scopus 로고    scopus 로고
    • Cosine transform based preconditioners for total variation minimization problems in image processing
    • Chan, R. H., Chan, T. F. and Wong, C., "Cosine transform based preconditioners for total variation minimization problems in image processing", Iterative Methods in Linear Algebra, II, V3,
    • Iterative Methods in Linear Algebra , vol.2
    • Chan, R.H.1    Chan, T.F.2    Wong, C.3
  • 8
    • 0002520370 scopus 로고
    • The circulant operator in the Banach algebra of matrices
    • Chan, R. H., Jin, X. and Yeung, M. C. (1991). "The circulant operator in the Banach algebra of matrices", Linear Algebra Appl., 149, 41-53.
    • (1991) Linear Algebra Appl. , vol.149 , pp. 41-53
    • Chan, R.H.1    Jin, X.2    Yeung, M.C.3
  • 9
    • 0345910458 scopus 로고
    • Circulant preconditioned Toeplitz least squares iterations
    • Chan, R. H., Nagy, J. and Plemmons, R. (1994). "Circulant preconditioned Toeplitz least squares iterations", SIAM J. Matrix Anal. Appl., 15, 80-97.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 80-97
    • Chan, R.H.1    Nagy, J.2    Plemmons, R.3
  • 10
    • 0030246195 scopus 로고    scopus 로고
    • Conjugate gradient methods for Toeplitz systems
    • Chan, R. H. and Ng, M. (1996). "Conjugate gradient methods for Toeplitz systems", SIAM Rev., 38, 427-482.
    • (1996) SIAM Rev. , vol.38 , pp. 427-482
    • Chan, R.H.1    Ng, M.2
  • 11
    • 0001589542 scopus 로고
    • Fast band-Toeplitz preconditioners for Hermitian Toeplitz systems
    • Chan, R. H. and Tang, P. (1994). "Fast band-Toeplitz preconditioners for Hermitian Toeplitz systems", SIAM J. Sci. Comp., 15, 164-171.
    • (1994) SIAM J. Sci. Comp. , vol.15 , pp. 164-171
    • Chan, R.H.1    Tang, P.2
  • 12
    • 0004175163 scopus 로고
    • John Wiley and Sons, New York
    • Davis, P. (1979). Circulant Matrices. John Wiley and Sons, New York.
    • (1979) Circulant Matrices
    • Davis, P.1
  • 13
    • 0039447646 scopus 로고    scopus 로고
    • A unifying approach to abstract matrix algebra preconditioning
    • Di Benedetto, F. and Serra Capizzano, S. (1999). "A unifying approach to abstract matrix algebra preconditioning", Numer. Math., 82-1, 57-90.
    • (1999) Numer. Math. , vol.82 , Issue.1 , pp. 57-90
    • Di Benedetto, F.1    Serra Capizzano, S.2
  • 16
    • 0001415134 scopus 로고
    • The condition of Vandennonde-like matrices involving orthogonal polynomials
    • Gautschi, W. (1983). "The condition of Vandennonde-like matrices involving orthogonal polynomials", Linear Algebra Appl., 52/53, 293-300.
    • (1983) Linear Algebra Appl. , vol.52-53 , pp. 293-300
    • Gautschi, W.1
  • 21
    • 0000137080 scopus 로고    scopus 로고
    • Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques
    • Hanke, M. and Nagy, J. (1996). "Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques", Inverse Problems, 12, 157-173.
    • (1996) Inverse Problems , vol.12 , pp. 157-173
    • Hanke, M.1    Nagy, J.2
  • 22
    • 0000859514 scopus 로고
    • Some aspects of circulant preconditioners
    • Huckle, T. (1993). "Some aspects of circulant preconditioners", SIAM J. Sci. Comp., 14, 531-541.
    • (1993) SIAM J. Sci. Comp. , vol.14 , pp. 531-541
    • Huckle, T.1
  • 24
    • 0029715230 scopus 로고    scopus 로고
    • Displacement structure approach to discrete-trigonometric-transform based preconditioners of G. Strang type and T. Chan type
    • Proc. "Workshop on Toeplitz Matrices" Cortona (Italy), September, 1996;
    • Kailath, T. and Olshevsky, V. (1996). "Displacement structure approach to discrete-trigonometric-transform based preconditioners of G. Strang type and T. Chan type", Proc. "Workshop on Toeplitz Matrices" Cortona (Italy), September, 1996; Calcolo, 33, 191-208.
    • (1996) Calcolo , vol.33 , pp. 191-208
    • Kailath, T.1    Olshevsky, V.2
  • 29
    • 0003274090 scopus 로고    scopus 로고
    • Toeplitz matrices and control theory
    • (R. Preuss, 118 Chandler Str., Suite 3, Boston MA 02116 USA), private communication Santa Barbara (CA), August
    • Preuss, R., "Toeplitz matrices and control theory", (R. Preuss, 118 Chandler Str., Suite 3, Boston MA 02116 USA), private communication at "Workshop on Toeplitz matrices in Filtering and Control", Santa Barbara (CA), August, 1996.
    • (1996) Workshop on Toeplitz Matrices in Filtering and Control
    • Preuss, R.1
  • 30
    • 0033445967 scopus 로고    scopus 로고
    • A Korovkin-type Theory for finite Toeplitz operators via matrix algebras
    • Serra, S. (1999). "A Korovkin-type Theory for finite Toeplitz operators via matrix algebras", Numer. Math., 82-1, 117-142.
    • (1999) Numer. Math. , vol.82 , Issue.1 , pp. 117-142
    • Serra, S.1
  • 31
    • 0033480798 scopus 로고    scopus 로고
    • The rate of convergence of Toeplitz based PCG methods for second order nonlinear boundary value problems
    • Serra, S. (1999). "The rate of convergence of Toeplitz based PCG methods for second order nonlinear boundary value problems", Numer. Math., 81-3, 461-495.
    • (1999) Numer. Math. , vol.81 , Issue.3 , pp. 461-495
    • Serra, S.1
  • 32
    • 0032216890 scopus 로고    scopus 로고
    • Toeplitz preconditioners constructed from linear approximation processes
    • Serra Capizzano, S. (1998). "Toeplitz preconditioners constructed from linear approximation processes", SIAM J. Matrix Anal. Appl., 20-2, 446-465.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.20 , Issue.2 , pp. 446-465
    • Serra Capizzano, S.1
  • 33
    • 0011258717 scopus 로고    scopus 로고
    • A Korovkin based approximation of multilevel Toeplitz matrices (with rectangular unstructured blocks) via multilevel Trigonometric matrix spaces
    • Serra Capizzano, S. (1999). "A Korovkin based approximation of multilevel Toeplitz matrices (with rectangular unstructured blocks) via multilevel Trigonometric matrix spaces", SIAM J. Numer. Anal., 36-6, 1831-1857.
    • (1999) SIAM J. Numer. Anal. , vol.36 , Issue.6 , pp. 1831-1857
    • Serra Capizzano, S.1
  • 34
    • 0000935389 scopus 로고    scopus 로고
    • Korovkin Theorems and linear positive Gram matrix algebras approximation of Toeplitz matrices
    • Serra Capizzano, S. (1998). "Korovkin Theorems and linear positive Gram matrix algebras approximation of Toeplitz matrices", Linear Algebra Appl., 284, 307-334.
    • (1998) Linear Algebra Appl. , vol.284 , pp. 307-334
    • Serra Capizzano, S.1
  • 36
    • 0033632284 scopus 로고    scopus 로고
    • Any Circulant-like preconditioner for multilevel matrices is not superlinear
    • Serra Capizzano, S. and Tyrtyshnikov, E. (1999). "Any Circulant-like preconditioner for multilevel matrices is not superlinear", SIAM J. Matrix Anal. Appl., 21-2, 431-439.
    • (1999) SIAM J. Matrix Anal. Appl. , vol.21 , Issue.2 , pp. 431-439
    • Serra Capizzano, S.1    Tyrtyshnikov, E.2
  • 37
    • 0010750876 scopus 로고    scopus 로고
    • A note on the spectral distribution of Toeplitz matrices
    • Tilli, P. (1998). "A note on the spectral distribution of Toeplitz matrices", Linear Multilin. Algebra, 45, 147-159.
    • (1998) Linear Multilin. Algebra , vol.45 , pp. 147-159
    • Tilli, P.1
  • 38
    • 0000415943 scopus 로고
    • Optimal and superoptimal circulant preconditioners
    • Tyrtyshnikov, E. (1992). "Optimal and superoptimal circulant preconditioners", SIAM J. Matrix Anal. Appl., 13, 459-473.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 459-473
    • Tyrtyshnikov, E.1
  • 39
    • 0039480616 scopus 로고
    • Circulant preconditioners with unbounded inverses
    • Tyrtyshnikov, E. (1995). "Circulant preconditioners with unbounded inverses", Linear Algebra Appl., 216, 1-23.
    • (1995) Linear Algebra Appl. , vol.216 , pp. 1-23
    • Tyrtyshnikov, E.1
  • 40
    • 3042570112 scopus 로고    scopus 로고
    • A unifying approach to some old and new theorems on distribution and clustering
    • Tyrtyshnikov, E. (1996). "A unifying approach to some old and new theorems on distribution and clustering", Linear Algebra Appl., 232, 1-43.
    • (1996) Linear Algebra Appl. , vol.232 , pp. 1-43
    • Tyrtyshnikov, E.1
  • 41
    • 0042855353 scopus 로고    scopus 로고
    • Spectra of multilevel Toeplitz matrices: Advanced theory via simple matrix relationships
    • Tyrtyshnikov, E. and Zamarashkin, N. (1998). "Spectra of multilevel Toeplitz matrices: advanced theory via simple matrix relationships", Linear Algebra Appl., 270, 15-27.
    • (1998) Linear Algebra Appl. , vol.270 , pp. 15-27
    • Tyrtyshnikov, E.1    Zamarashkin, N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.