메뉴 건너뛰기




Volumn 34, Issue 1, 2012, Pages

A matrix-free approach for solving the parametric gaussian process maximum likelihood problem

Author keywords

Circulant preconditioner; Fast multipole method; Gaussian process; Maximum likelihood estimation; Preconditioned conjugate gradient; Ssample average approximation; Toeplitz system

Indexed keywords

COVARIANCE MATRIX; GAUSSIAN DISTRIBUTION; GAUSSIAN NOISE (ELECTRONIC); STOCHASTIC PROGRAMMING; STOCHASTIC SYSTEMS;

EID: 84861377864     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/110831143     Document Type: Article
Times cited : (70)

References (34)
  • 1
    • 33846349887 scopus 로고
    • A hierarchical O(N logN) force-calculation algorighm
    • J. Barnes and P. Hut, A hierarchical O(N logN) force-calculation algorighm, Nature, 324 (1986), pp. 446-449.
    • (1986) Nature , vol.324 , pp. 446-449
    • Barnes, J.1    Hut, P.2
  • 3
    • 0002520370 scopus 로고
    • The circulant operator in the Banach algebra of matrices
    • R. H. Chan, X.-Q. Jin, and M.-C. Yeung, The circulant operator in the Banach algebra of matrices, Linear Algebra Appl., 149 (1991), pp. 41-53.
    • (1991) Linear Algebra Appl. , vol.149 , pp. 41-53
    • Chan, R.H.1    Jin, X.-Q.2    Yeung, M.-C.3
  • 4
    • 0000853646 scopus 로고
    • An optimal circulant preconditioner for Toeplitz systems
    • T. F. Chan, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Statist. Comput., 9 (1988), pp. 766-771.
    • (1988) SIAM J. Sci. Statist. Comput. , vol.9 , pp. 766-771
    • Chan, T.F.1
  • 5
    • 79952297521 scopus 로고    scopus 로고
    • Computing f(A)b via least squares polynomial approximations
    • J. Chen, M. Anitescu, and Y. Saad, Computing f(A)b via least squares polynomial approximations, SIAM J. Sci. Comput., 33 (2011), pp. 195-222.
    • (2011) SIAM J. Sci. Comput. , vol.33 , pp. 195-222
    • Chen, J.1    Anitescu, M.2    Saad, Y.3
  • 9
    • 84861370819 scopus 로고    scopus 로고
    • An adaptive treecode for computing nonbounded potential energy in classical molecular systems
    • Z. Duan and R. Krasny, An adaptive treecode for computing nonbounded potential energy in classical molecular systems, J. Comput. Chem., 23 (2001), pp. 1549-1571.
    • (2001) J. Comput. Chem. , vol.23 , pp. 1549-1571
    • Duan, Z.1    Krasny, R.2
  • 10
    • 11444252972 scopus 로고    scopus 로고
    • A Krylov subspace algorithm for multiquadric interpolation in many dimensions
    • DOI 10.1093/imanum/drh021
    • A. C. Faul, G. Goodsell, and M. J. D. Powell, A Krylov subspace algorithm for multiquadric interpolation in many dimensions, IMA J. Numer. Anal., 25 (2005), pp. 1-24. (Pubitemid 40083525)
    • (2005) IMA Journal of Numerical Analysis , vol.25 , Issue.1 , pp. 1-24
    • Faul, A.C.1    Goodsell, G.2    Powell, M.J.D.3
  • 14
    • 52649096416 scopus 로고    scopus 로고
    • Fast radial basis function interpolation via preconditioned Krylov iteration
    • N. A. Gumerov and R. Duraiswami, Fast radial basis function interpolation via preconditioned Krylov iteration, SIAM J. Sci. Comput., 29 (2007), pp. 1876-1899.
    • (2007) SIAM J. Sci. Comput. , vol.29 , pp. 1876-1899
    • Gumerov, N.A.1    Duraiswami, R.2
  • 18
    • 16244384565 scopus 로고    scopus 로고
    • Combining field data and computer simulations for calibration and prediction
    • D. Higdon, M. Kennedy, J. Cavendish, J. Cafeo, and R. Ryne, Combining field data and computer simulations for calibration and prediction, SIAM J. Sci. Comput., 26 (2004), pp. 448-466.
    • (2004) SIAM J. Sci. Comput. , vol.26 , pp. 448-466
    • Higdon, D.1    Kennedy, M.2    Cavendish, J.3    Cafeo, J.4    Ryne, R.5
  • 19
    • 0001264981 scopus 로고
    • A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines
    • M. Hutchinson, A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines., Comm. Statist. Simulations Comput., 19 (1990), pp. 433-450.
    • (1990) Comm. Statist. Simulations Comput. , vol.19 , pp. 433-450
    • Hutchinson, M.1
  • 21
    • 85140870012 scopus 로고    scopus 로고
    • Fast evaluation of multiquatric RBF sums by a Cartesian treecode
    • to appear.
    • R. Krasny and L. Wang, Fast evaluation of multiquatric RBF sums by a Cartesian treecode, SIAM Sci. Comput., to appear.
    • SIAM Sci. Comput.
    • Krasny, R.1    Wang, L.2
  • 22
    • 0035922241 scopus 로고    scopus 로고
    • A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow
    • DOI 10.1006/jcph.2001.6862
    • K. Lindsay and R. Krasny, A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow, J. Comput. Phys., 172 (2001), pp. 879-907. (Pubitemid 33082566)
    • (2001) Journal of Computational Physics , vol.172 , Issue.2 , pp. 879-907
    • Lindsay, K.1    Krasny, R.2
  • 23
    • 62849117436 scopus 로고    scopus 로고
    • A Cartesian treecode for screened Coulomb interactions
    • P. Li, H. Johnston, and R. Krasny, A Cartesian treecode for screened Coulomb interactions, J. Comput. Phys., 228 (2009), pp. 3858-3868.
    • (2009) J. Comput. Phys. , vol.228 , pp. 3858-3868
    • Li, P.1    Johnston, H.2    Krasny, R.3
  • 24
    • 34250122797 scopus 로고
    • Interpolation of scattered data: Distance matrices and conditionally positive definite functions
    • C. A. Micchelli, Interpolation of scattered data: Distance matrices and conditionally positive definite functions, Constr. Approx., 2 (1986), pp. 11-22.
    • (1986) Constr. Approx. , vol.2 , pp. 11-22
    • Micchelli, C.A.1
  • 25
    • 0343005865 scopus 로고
    • Variable block CG algorithms for solving large sparse symmetric positive definite linear systems on parallel computers, I: General iterative scheme
    • A. A. Nikishin and A. Y. Yeremin, Variable block CG algorithms for solving large sparse symmetric positive definite linear systems on parallel computers, I: General iterative scheme, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 1135-1153.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 1135-1153
    • Nikishin, A.A.1    Yeremin, A.Y.2
  • 27
    • 0001084178 scopus 로고
    • The block conjugate gradient algorithm and related methods
    • D. P. O'Leary, The block conjugate gradient algorithm and related methods, Linear Algebra Appl., 29 (1980), pp. 293-322.
    • (1980) Linear Algebra Appl. , vol.29 , pp. 293-322
    • O'Leary, D.P.1
  • 29
    • 70349920765 scopus 로고    scopus 로고
    • Efficient sampling for spatial uncertainty quantification in multibody system dynamics applications
    • K. P. Schmitt, M. Anitescu, and D. Negrut, Efficient sampling for spatial uncertainty quantification in multibody system dynamics applications, Internat. J. Numer. Methods Engrg., 80 (2009), pp. 537-564.
    • (2009) Internat. J. Numer. Methods Engrg. , vol.80 , pp. 537-564
    • Schmitt, K.P.1    Anitescu, M.2    Negrut, D.3
  • 34
    • 0000415943 scopus 로고
    • Optimal and superoptimal circulant preconditioners
    • E. E. Tyrtyshnikov, Optimal and superoptimal circulant preconditioners, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 459-173.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 459-173
    • Tyrtyshnikov, E.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.