Numerical Treatment of Inverse Problems in Differential and Integral Equations : Proceedings of an International Workshop, Heidelberg, Fed. Rep. of Germany, August 30 -- September 3, 1982

In many scientific or engineering applications, where ordinary differen­ tial equation (OOE),partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for prediction, monitoring, or control purposes. In many cases, however, successful simulation of a process must be preceded by the solution of the so-called inverse problem, which is usually more complex: given meas­ ured data and an associated theoretical model, determine unknown para­ meters in that model (or unknown functions to be parametrized) in such a way that some measure of the "discrepancy" between data and model is minimal. The present volume deals with the numerical treatment of such inverse probelms in fields of application like chemistry (Chap. 2,3,4, 7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20), geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation (Chap. 15,16), elctrocardiology (Chap. 14), computer tomography (Chap. 21), and control system design (Chap. 12,13). In the actual computational solution of inverse problems in these fields, the following typical difficulties arise: (1) The evaluation of the sen­ sitivity coefficients for the model. may be rather time and storage con­ suming. Nevertheless these coefficients are needed (a) to ensure (local) uniqueness of the solution, (b) to estimate the accuracy of the obtained approximation of the solution, (c) to speed up the iterative solution of nonlinear problems. (2) Often the inverse problems are ill-posed. To cope with this fact in the presence of noisy or incomplete data or inev­ itable discretization errors, regularization techniques are necessary. Front Matter....Pages i-xiii Front Matter....Pages 1-1 Smooth Numerical Solutions of Ordinary Differential Equations....Pages 2-12 Towards Parameter Identification for Large Chemical Reaction Systems....Pages 13-26 Identification of Rate Constants in Bistable Chemical Reactions....Pages 27-47 New Methods of Parameter Identification in Kinetics of Closed and Open Reaction Systems....Pages 48-61 On the Estimation of Small Perturbations in Ordinary Differential Equations....Pages 62-72 Front Matter....Pages 73-73 Multiple Shooting Techniques Revisited....Pages 74-94 Recent Advances in Parameteridentification Techniques for O.D.E.....Pages 95-121 Some Examples of Parameter Estimation by Multiple Shooting....Pages 122-136 Unrestricted Harmonic Balance III, Application to Running and Standing Chemical Waves....Pages 137-145 Inverse Eigenvalue Problems for the Mantle....Pages 146-149 Inverse Problem of Quantal Potential Scattering at Fixed Energy....Pages 150-160 An Inverse Eigenvalue Problem from Control Theory....Pages 161-170 Numerical Methods for Robust Eigenstructure Assignment in Control System Design....Pages 171-178 Front Matter....Pages 179-179 Some Inverse Problems in Electrocardiology....Pages 180-205 Determination of Coefficients in Reservoir Simulation....Pages 206-226 Identification of Nonlinear Soil Physical Parameters from an Input-Output Experiment....Pages 227-237 On an Inverse Non-Linear Diffusion Problem....Pages 238-245 The Numerical Solution of a Non-Characteristic Cauchy Probelm for a Parabolic Equation....Pages 246-268 The Inverse Problem in Geoelectrical Prospecting Assuming a Horizontally Layered Half-Space....Pages 269-277 Two Dimensional Velocity Inversion for Acoustic Waves with Incomplete Information....Pages 278-287 Front Matter....Pages 289-289 Exploiting the Ranges of Radon Transformsin Tomography....Pages 290-303 Regularization Techniques for Inverse Problems in Molecular Biology....Pages 304-319 A Comparison of Statistical Regularization and Fourier Extrapolation Methods for Numerical Deconvolution....Pages 320-334 Deconvolution of Gaussian and Other Kernels....Pages 335-344 Regularization by Least-Squares Collocation....Pages 345-354 Back Matter....Pages 355-357 In many scientific or engineering applications, where ordinary differenƯ tial equation (OOE), partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for prediction, monitoring, or control purposes. In many cases, however, successful simulation of a process must be preceded by the solution of the so-called inverse problem, which is usually more complex: given measƯ ured data and an associated theoretical model, determine unknown paraƯ meters in that model (or unknown functions to be parametrized) in such a way that some measure of the "discrepancy" between data and model is minimal. The present volume deals with the numerical treatment of such inverse probelms in fields of application like chemistry (Chap. 2,3,4, 7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20), geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation (Chap. 15,16), elctrocardiology (Chap. 14), computer tomography (Chap. 21), and control system design (Chap. 12,13). In the actual computational solution of inverse problems in these fields, the following typical difficulties arise: (1) The evaluation of the senƯ sitivity coefficients for the model. may be rather time and storage conƯ suming. Nevertheless these coefficients are needed (a) to ensure (local) uniqueness of the solution, (b) to estimate the accuracy of the obtained approximation of the solution, (c) to speed up the iterative solution of nonlinear problems. (2) Often the inverse problems are ill-posed. To cope with this fact in the presence of noisy or incomplete data or inevƯ itable discretization errors, regularization techniques are necessary