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  • AMS (MOS): 65D25  (1)
  • Numerical Methods  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 48 (1986), S. 671-697 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65D25 ; 65D10 ; CR: G1.2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We investigate the statistical methods of cross-validation (CV) and maximum-likelihood (ML) for estimating optimal regularization parameters in the numerical differentiation and smoothing of non-exact data. Various criteria for optimality are examined, and the (asymptotic) notions of strong optimality, weak optimality and suboptimality are introduced relative to these criteria. By restricting attention to certainN-dimensional Hilbert spaces of smooth and stochastic functions, whereN is the number of data, we give regularity conditions on the data under which λCV, the regularization parameter predicted by CV, is strongly optimal with respect to the predictive mean-square signal error. We show that λML is at best weakly optimal with respect to this criterion but is strongly optimal with respect to the innovation variance of the data. For numerical differentiation, λCV and λML are both shown to be suboptimal with respect to the predictive mean-square derivative error.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 691-710 
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new pseudospectral method for simulating transient viscoelastic flows is presented. The governing equations are a system of seven first-order equations of mixed type. The essential features of the method are (i) all seven independent flow variables are represented on a common Chebyshev-Gauss-Lobatto grid; (ii) the pressure is treated in such a way as to give a globally divergence-free velocity field, i.e., the divergence of the velocity field vanishes globally within the region, and (iii) different time scales pertaining within the hyperbolic constitutive equations are treated using the splitting technique of LeVeque and Yee originally proposed in a finite-difference context. The method is applied to transient axisymmetric flow of an Oldroyd B fluid in a channel formulated in two ways: (I) as an initial boundary-value problem, and (II) as a body-force problem. © 1993 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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