메뉴 건너뛰기




Volumn 31, Issue 5, 2010, Pages 2681-2699

Spectral methods for parameterized matrix equations

Author keywords

Parameterized systems; Spectral methods

Indexed keywords

ANALYTICITY; CLASSICAL THEORY; ERROR ESTIMATES; INFINITE SYSTEM; INTERPOLATORY; LINEAR SYSTEM OF EQUATIONS; MATRIX; MATRIX EQUATIONS; NUMERICAL EXAMPLE; PARAMETERIZED; PARAMETERIZED SYSTEM; PSEUDOSPECTRAL METHODS; RESIDUAL ERROR; RIGHT-HAND SIDES; SPECTRAL METHODS; VECTOR-VALUED FUNCTION;

EID: 79251523176     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/090755965     Document Type: Article
Times cited : (25)

References (32)
  • 1
    • 0035964634 scopus 로고    scopus 로고
    • Solution of stochastic partial differential equations using Galerkin finite element techniques
    • I. Babuška, M. K. Deb, and J. T. Oden, Solution of stochastic partial differential equations using Galerkin finite element techniques, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 6359-6372.
    • (2001) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 6359-6372
    • Babuška, I.1    Deb, M.K.2    Oden, J.T.3
  • 2
    • 34548216854 scopus 로고    scopus 로고
    • A stochastic collocation method for elliptic partial differential equations with random input data
    • I. Babuška, F. Nobile, and R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data, SIAM J. Numer. Anal., 45 (2007), pp. 1005-1034.
    • (2007) SIAM J. Numer. Anal. , vol.45 , pp. 1005-1034
    • Babuška, I.1    Nobile, F.2    Tempone, R.3
  • 3
    • 13844319204 scopus 로고    scopus 로고
    • Galerkin finite element approximations of stochastic elliptic partial differential equations
    • I. Babuška, R. Tempone, and G. E. Zouraris, Galerkin finite element approximations of stochastic elliptic partial differential equations, SIAM J. Numer. Anal., 42 (2004), pp. 800-825.
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 800-825
    • Babuška, I.1    Tempone, R.2    Zouraris, G.E.3
  • 6
    • 34247383235 scopus 로고    scopus 로고
    • The PageRank vector: Properties computation approximation and acceleration
    • C. Brezinski and M. Redivo-Zaglia, The PageRank vector: Properties, computation, approximation, and acceleration, SIAM J. Matrix Anal. Appl., 28 (2006), pp. 551-575.
    • (2006) SIAM J.Matrix Anal. Appl. , vol.28 , pp. 551-575
    • Brezinski, C.1    Redivo-Zaglia, M.2
  • 9
    • 78650761166 scopus 로고    scopus 로고
    • Nonlinear least squares and super resolution
    • J. Chung and J. G. Nagy, Nonlinear least squares and super resolution, J. Phys. Conf. Ser., 124 (2008), p. 012019.
    • (2008) J. Phys. Conf. Ser. , vol.124 , pp. 012019
    • Chung, J.1    Nagy, J.G.2
  • 11
    • 0142169393 scopus 로고    scopus 로고
    • Lyapunov exponents of systems evolving on quadratic groups
    • L. Dieci and L. Lopez, Lyapunov exponents of systems evolving on quadratic groups, SIAM J. Matrix Anal. Appl., 24 (2003), pp. 1175-1185.
    • (2003) SIAM J. Matrix Anal. Appl. , vol.24 , pp. 1175-1185
    • Dieci, L.1    Lopez, L.2
  • 12
    • 12344334601 scopus 로고    scopus 로고
    • Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering
    • H. C. Elman, O. G. Ernst, D. P. O'Leary, and M. Stewart, Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering, Comput. Methods Appl. Mech. Engrg., 194 (2005), pp. 1037-1055.
    • (2005) Comput. Methods Appl. Mech. Engrg. , vol.194 , pp. 1037-1055
    • Elman, H.C.1    Ernst, O.G.2    O'Leary, D.P.3    Stewart, M.4
  • 13
    • 67649534729 scopus 로고    scopus 로고
    • Efficient solvers for a linear stochastic Galerkin mixed formulation of diffusion problems with random data
    • O. G. Ernst, C. E. Powell, D. J. Silvester, and E. Ullmann, Efficient solvers for a linear stochastic Galerkin mixed formulation of diffusion problems with random data, SIAM J. Sci. Comput., 31 (2009), pp. 1424-1447.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 1424-1447
    • Ernst, O.G.1    Powell, C.E.2    Silvester, D.J.3    Ullmann, E.4
  • 14
  • 15
    • 2942620338 scopus 로고    scopus 로고
    • The interplay between classical analyses and (numerical) linear algebra-A tribute to Gene Golub
    • W. Gautschi, The interplay between classical analyses and (numerical) linear algebra-A tribute to Gene Golub, Electron. Trans. Numer. Anal., 13 (2002), pp. 119-147.
    • (2002) Electron. Trans. Numer. Anal. , vol.13 , pp. 119-147
    • Gautschi, W.1
  • 20
    • 0003229172 scopus 로고
    • Numerical analysis of spectral methods: Theory and applications
    • Philadelphia
    • D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, 1977.
    • (1977) SIAM
    • Gottlieb, D.1    Orszag, S.A.2
  • 23
    • 77956037695 scopus 로고    scopus 로고
    • The Lanczos method for parameterized symmetric linear systems with multiple right-hand sides
    • K. Meerbergen and Z. Bai, The Lanczos method for parameterized symmetric linear systems with multiple right-hand sides, J. Matrix Anal. Appl., 31 (2010), pp. 1642-1662.
    • (2010) J. Matrix Anal. Appl. , vol.31 , pp. 1642-1662
    • Meerbergen, K.1    Bai, Z.2
  • 25
    • 0025620076 scopus 로고
    • Kriging: A method of interpolation for geographical information systems
    • M. Oliver and R. Webster, Kriging: A method of interpolation for geographical information systems, Internat. J. Geograph. Inform. Sci., 4 (1990), pp. 313-332.
    • (1990) Internat. J. Geograph. Inform. Sci. , vol.4 , pp. 313-332
    • Oliver, M.1    Webster, R.2
  • 27
    • 65249182525 scopus 로고    scopus 로고
    • Block-diagonal preconditioning for spectral stochastic finite-element systems
    • C. E. Powell and H. C. Elman, Block-diagonal preconditioning for spectral stochastic finite-element systems, IMA J. Numer. Anal., 29 (2009), pp. 350-375.
    • (2009) IMA J. Numer. Anal. , vol.29 , pp. 350-375
    • Powell, C.E.1    Elman, H.C.2
  • 29
    • 0004073954 scopus 로고
    • American Mathematical Society Providence, RI
    • G. Szegö, Orthogonal Polynomials, American Mathematical Society, Providence, RI, 1939.
    • (1939) Orthogonal Polynomials
    • Szegö, G.1
  • 30
    • 77649135434 scopus 로고    scopus 로고
    • A rational interpolation scheme with superpolynomial rate of convergence
    • Q. Wang, P. Moin, and G. Iaccarino, A rational interpolation scheme with superpolynomial rate of convergence, SIAM J. Numer. Anal., 47 (2010), pp. 4073-4097.
    • (2010) SIAM J. Numer. Anal. , vol.47 , pp. 4073-4097
    • Wang, Q.1    Moin, P.2    Iaccarino, G.3
  • 31
    • 33646577797 scopus 로고    scopus 로고
    • High-order collocation methods for differential equations with random inputs
    • D. Xiu and J. S. Hesthaven, High-order collocation methods for differential equations with random inputs, SIAM J. Sci. Comput., 27 (2005), pp. 1118-1139.
    • (2005) SIAM J. Sci. Comput. , vol.27 , pp. 1118-1139
    • Xiu, D.1    Hesthaven, J.S.2
  • 32
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • D. Xiu and G. E. Karniadakis, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput., 24 (2002), pp. 619-644.
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.