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  • 1
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    Estimation of discontinuous coefficients and boundary parameters for hyperbolic systems (1986)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The problem of estimating discontinuous coefficients, including locations of discontinuities, that occur in second order hyperbolic systems typical of those arising in I-D surface seismic problems is discussed. In addition, the problem of identifying unknown parameters that appear in boundary conditions for the system is treated. A spline-based approximation theory is presented, together with related convergence findings and representative numerical examples.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-178133 , NAS 1.26:178133 , ICASE-86-43
    Format: application/pdf
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  • 2
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    Estimation of coefficients and boundary parameters in hyperbolic systems (1984)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Semi-discrete Galerkin approximation schemes are considered in connection with inverse problems for the estimation of spatially varying coefficients and boundary condition parameters in second order hyperbolic systems typical of those arising in 1-D surface seismic problems. Spline based algorithms are proposed for which theoretical convergence results along with a representative sample of numerical findings are given.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-172389 , ICASE-84-24 , NAS 1.26:172389
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  • 3
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    Computational methods for estimation of parameters in hyperbolic systems (1983)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-172234 , ICASE-83-53 , NAS 1.26:172234
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  • 4
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    Estimation of time- and state-dependent delays and other parameters in functional differential equations (1990)
    In:  Other Sources
    Details
    Publication Date: 2019-07-12
    Description: A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.
    Keywords: NUMERICAL ANALYSIS
    Type: SIAM Journal on Applied Mathematics (ISSN 0036-1399); 50; 972-1000
    Format: text
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  • 5
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    Parameter estimation in moving boundary problems (1988)
    In:  Other Sources
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    Publication Date: 2019-07-12
    Description: An approximation scheme which can be used to estimate unknown parameters in moving boundary problems is described. The model equations are fairly general nonlinear diffusion/reaction equations of one spatial variable. Conditions on the parameter sets and model equations are given. It is shown that the estimates obtained using the approximations will converge to best-fit parameters for the original model equations.
    Keywords: NUMERICAL ANALYSIS
    Type: Applied Mathematics Letters (ISSN 0893-9659); 1; 3 19
    Format: text
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