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SUMMARY In this paper, several boundary element regularization methods, such as iterative, conjugate gradient, Tikhonov regularization and singular value decomposition methods, for solving the Cauchy problem associated to the Helmholtz equation are developed and compared. Regularizing stopping criteria are developed and the convergence, as well as the(More)
PURPOSE Model fitting of dynamic contrast-enhanced-magnetic resonance imaging-MRI data with nonlinear least squares (NLLS) methods is slow and may be biased by the choice of initial values. The aim of this study was to develop and evaluate a linear least squares (LLS) method to fit the two-compartment exchange and -filtration models. METHODS A(More)
The analytical solutions for linear, one-dimensional, time-dependent partial differential equations subject to initial or lateral boundary conditions are reviewed and obtained in the form of convergent Adomian decomposition power series with easily computable components. The efficiency and power of the technique are shown for wide classes of equations of(More)
In this paper the determination of the spacewise dependent material property coefficients and the function solution in both steady and unsteady diffusion problems are analysed. For a one-dimensional quasi-heterogeneous material with square-root harmonic conductivity it is shown that a single measurement of the conductivity and the flux on the boundary is(More)