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Volumn 32, Issue 2, 2010, Pages 774-792

Shift-invert arnoldi approximation to the toeplitz matrix exponential

Author keywords

Krylov subspace; Matrix exponential; Numerical range; Shift invert Arnoldi method; Toeplitz matrix

Indexed keywords

MATRIX ALGEBRA; NUMERICAL METHODS;

EID: 77950848559     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/090758064     Document Type: Article
Times cited : (58)

References (33)
  • 1
    • 0037170714 scopus 로고    scopus 로고
    • On a method for solving an integral equation in the displacement contact problem
    • DOI 10.1016/S0096-3003(01)00003-0, PII S0096300301000030
    • M. ABDOU AND A. BADR, On a method for solving an integral equation in the displacement contact problem, Appl. Math. Comput., 127 (2002), pp. 65-78. (Pubitemid 34116070)
    • (2002) Applied Mathematics and Computation , vol.127 , Issue.1 , pp. 65-78
    • Abdou, M.A.1    Badr, A.A.2
  • 2
    • 0003090115 scopus 로고
    • Superfast solution of real positive definite Toeplitz systems
    • G. AMMAR AND W. GRAGG, Superfast solution of real positive definite Toeplitz systems,SlAM J. Matrix Anal. Appl., 9 (1988), pp. 61-76.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 61-76
    • Ammar, G.1    Gragg, W.2
  • 4
    • 0034382829 scopus 로고    scopus 로고
    • Efficient computation of the exponential operator for large, sparse, symmetric matrices
    • L. BERGAMASCHI AND M. VIANELLO, Efficient computation of the exponential operator for large, sparse, symmetric matrices, Numer. Linear Algebra Appl., 7 (2000), pp. 27-45.
    • (2000) Numer. Linear Algebra Appl. , vol.7 , pp. 27-45
    • Bergamaschi, L.1    Vianello, M.2
  • 6
    • 0030246195 scopus 로고    scopus 로고
    • Conjugate gradient methods for Toeplitz systems
    • R. CHAN AND M. NG, Conjugate gradient methods for Toeplitz systems, SIAM Rev., 38 (1996), pp. 427-482. (Pubitemid 126599620)
    • (1996) SIAM Review , vol.38 , Issue.3 , pp. 427-482
    • Chan, R.H.1    Michael, K.N.G.2
  • 8
    • 70449371467 scopus 로고    scopus 로고
    • Error estimates for polynomial krylov approximations to matrix functions
    • F. DIELE,I.MORET,AND S. RAGNI, Error estimates for polynomial Krylov approximations to matrix functions, SIAM. J. Matrix Anal. Appl., 30 (2008), pp. 1546-1565.
    • (2008) SIAM. J. Matrix Anal. Appl. , vol.30 , pp. 1546-1565
    • Diele, F.1    Moret, I.2    Ragni, S.3
  • 9
    • 37849029848 scopus 로고    scopus 로고
    • A restarted Krylov subspace method for the evaluation of matrix functions
    • M. ElERMANN AND O. ERNST, A restarted Krylov subspace method for the evaluation of matrix functions, SIAM J. Numer. Anal., 44 (2006), pp. 2481-2504.
    • (2006) SIAM J. Numer. Anal. , vol.44 , pp. 2481-2504
    • Elermann, M.1    Ernst, O.2
  • 10
    • 33646928736 scopus 로고    scopus 로고
    • Preconditioning Lanczos approximations to the matrix exponential
    • DOI 10.1137/040605461
    • J. VAN DEN ESHOF AND M. HOCHBRUCK, Preconditioning Lanczos approximations to the matrix exponential, SIAM J. Sci. Comput., 27 (2006), pp. 1438-1457. (Pubitemid 44077334)
    • (2006) SIAM Journal of Scientific Computing , vol.27 , Issue.4 , pp. 1438-1457
    • Van Den Eshof, J.1    Hochbruck, M.2
  • 11
    • 49749118692 scopus 로고    scopus 로고
    • Stopping criteria for rational matrix functions of Hermitian and symmetric matrices
    • A. FROMMER AND V. SIMONCINI, Stopping criteria for rational matrix functions of Hermitian and symmetric matrices, SIAM J. Sci. Comput., 30 (2008), pp. 1387-1412.
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 1387-1412
    • Frommer, A.1    Simoncini, V.2
  • 12
    • 0000269389 scopus 로고
    • Efficient solution of parabolic equations by Krylov approximation methods
    • E. GALLOPOULOS AND Y. SAAD, Efficient solution of parabolic equations by Krylov approximation methods, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 1236-1264.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 1236-1264
    • Gallopoulos, E.1    Saad, Y.2
  • 13
    • 0001726473 scopus 로고
    • On the inversion of finite Toeplitz matrices and their continuous analogs
    • I. GOHBERG AND A. SEMENCUL, On the inversion of finite Toeplitz matrices and their continuous analogs, Mat. Issled., 2 (1972), pp. 201-233.
    • (1972) Mat. Issled. , vol.2 , pp. 201-233
    • Gohberg, I.1    Semencul, A.2
  • 14
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed., The John Hopkins University Press, Baltimore
    • G. GOLUB AND C. VAN LOAN, Matrix Computations, 3rd ed., The John Hopkins University Press, Baltimore, 1996.
    • (1996) Matrix Computations
    • Golub, G.1    Van Loan, C.2
  • 16
    • 27144549311 scopus 로고    scopus 로고
    • The scaling and squaring method for the matrix exponential revisited
    • DOI 10.1137/04061101X
    • N. HIGHAM, The scaling and squaring method for the matrix exponential revisited, SIAM J. Matrix Anal. Appl., 26 (2005), pp. 1179-1193. (Pubitemid 41495317)
    • (2005) SIAM Journal on Matrix Analysis and Applications , vol.26 , Issue.4 , pp. 1179-1193
    • Higham, N.J.1
  • 17
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov Subspace Approximations to the Matrix Exponential Operator
    • M. HOCHBRUCK AND C. LUBICH, On Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal., 34 (1997), pp. 1911-1925. (Pubitemid 127463577)
    • (1997) SIAM Journal on Numerical Analysis , vol.34 , Issue.5 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, C.2
  • 18
    • 33845347760 scopus 로고    scopus 로고
    • Analysis of projection methods for rational function approximation to the matrix exponential
    • DOI 10.1137/05062590
    • L. LOPEZ AND V. SIMONCINI, Analysis of projection methods for rational function approximation to the matrix exponential, SIAM J. Numer. Anal., 44 (2006), pp. 613-635. (Pubitemid 46622339)
    • (2006) SIAM Journal on Numerical Analysis , vol.44 , Issue.2 , pp. 613-635
    • Lopez, L.1    Simoncini, V.2
  • 19
    • 34248474317 scopus 로고
    • Option pricing when underlying stock returns are discontinuous
    • R. MERTON, Option pricing when underlying stock returns are discontinuous, J. Financ. Econ., 3 (1976), pp. 125-144.
    • (1976) J. Financ. Econ. , vol.3 , pp. 125-144
    • Merton, R.1
  • 20
    • 0001143041 scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix
    • C. MoLER AND C. VAN LOAN, Nineteen dubious ways to compute the exponential of a matrix, SIAM Rev., 20 (1978), pp. 801-836.
    • (1978) SIAM Rev. , vol.20 , pp. 801-836
    • Moler, C.1    Van Loan, C.2
  • 21
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later
    • C. MOLER AND C. VAN LOAN, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev., 45 (2003), pp. 3-49.
    • (2003) SIAM Rev. , vol.45 , pp. 3-49
    • Moler, C.1    Van Loan, C.2
  • 22
    • 34248578148 scopus 로고    scopus 로고
    • On RD-rational Krylov approximations to the core-functions of exponential integrators
    • I. MoRET, On RD-rational Krylov approximations to the core-functions of exponential integrators, Numer. Linear Algebra Appl., 14 (2007), pp. 445-457.
    • (2007) Numer. Linear Algebra Appl. , vol.14 , pp. 445-457
    • Moret, I.1
  • 23
    • 0035360316 scopus 로고    scopus 로고
    • An interpolatory approximation of the matrix exponential based on Faber polynomials
    • DOI 10.1016/S0377-0427(00)00261-2, PII S0377042700002612
    • I. MoRET AND P. NovATI, An interpolatory approximation of the matrix exponential based on Faber polynomials, J. Comput. Appl. Math., 131 (2001), pp. 361-380. (Pubitemid 32621155)
    • (2001) Journal of Computational and Applied Mathematics , vol.131 , Issue.1-2 , pp. 361-380
    • Moret, I.1    Novati, P.2
  • 24
    • 8144228833 scopus 로고    scopus 로고
    • RD-rational approximations of the matrix exponential
    • DOI 10.1023/B:BITN.0000046805.27551.3b
    • I. MoRET AND P. NovATI, RD-rational approximations of the matrix exponential,BIT, 44 (2004), pp. 595-615. (Pubitemid 39473828)
    • (2004) BIT Numerical Mathematics , vol.44 , Issue.3 , pp. 595-615
    • Moret, I.1    Novati, P.2
  • 25
    • 0141940605 scopus 로고    scopus 로고
    • Recursive-based PCG methods for Toeplitz systems with nonnegative generating functions
    • M. NG, H. SUN, AND X. JIN, Recursive-based PCG methods for Toeplitz systems with nonnegative generating functions, SIAM J. Sci. Comput., 24 (2003), pp. 1507-1529.
    • (2003) SIAM J. Sci. Comput. , vol.24 , pp. 1507-1529
    • Ng, M.1    Sun, H.2    Jin, X.3
  • 26
    • 49749108595 scopus 로고    scopus 로고
    • Acceleration techniques for approximating the matrix exponential operator
    • M. POPOLIZIO AND V. SIMONCINI, Acceleration techniques for approximating the matrix exponential operator, SIAM J. Matrix Anal. Appl., 30 (2008), pp. 657-683.
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , pp. 657-683
    • Popolizio, M.1    Simoncini, V.2
  • 27
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • R. RoCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.1
  • 28
    • 0026818185 scopus 로고
    • Analysis of some Krylov subspace approximations to the matrix exponential operator
    • Y. SAAD, Analysis of some Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal., 29 (1992), pp. 209-228.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 209-228
    • Saad, Y.1
  • 30
    • 0029693004 scopus 로고    scopus 로고
    • Singular values and eigenvalues of non-Hermitian block Toeplitz matrices
    • S. SERRA CAPIZZANO AND P. TILLI, Extreme singular values and eigenvalues of non-Hermitian block Toeplitz matrices, J. Comput. Appl. Math., 108 (1999), pp. 113-130. (Pubitemid 126175960)
    • (1996) Calcolo , vol.33 , Issue.1-4 , pp. 58-69
    • Tilli, P.1
  • 31
    • 2342652956 scopus 로고    scopus 로고
    • Theory of inexact Krylov subspace methods and applications to scientific computing
    • V. SIMONCINI AND D. SZYLD, Theory of inexact Krylov subspace methods and applications to scientific computing, SIAM J. Sci. Comput., 25 (2003), pp. 454-477.
    • (2003) SIAM J. Sci. Comput. , vol.25 , pp. 454-477
    • Simoncini, V.1    Szyld, D.2
  • 32
    • 48249152125 scopus 로고    scopus 로고
    • Exponential time integration and Chebychev discretisation schemes for fast pricing of options
    • D. TANGMAN, A. GOPAUL, AND M. BHURUTH, Exponential time integration and Chebychev discretisation schemes for fast pricing ofoptions, Appl. Numer. Math., 58 (2008), pp. 1309-1319.
    • (2008) Appl. Numer. Math. , vol.58 , pp. 1309-1319
    • Tangman, D.1    Gopaul, A.2    Bhuruth, M.3
  • 33
    • 0042358811 scopus 로고    scopus 로고
    • Singular values and eigenvalues of non-Hermitian block Toeplitz matrices
    • PII S002437959700308X
    • P. TILLI, Singular values and eigenvalues of non-Hermitian block Toeplitz matrices,Linear Algebra Appl., 272 (1998), pp. 59-89. (Pubitemid 128392360)
    • (1998) Linear Algebra and Its Applications , vol.272 , Issue.1-3 , pp. 59-89
    • Tilli, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.