In this papert we discuss the inverse problem of 1-dimensional acoustic wave equation and propose an approximate inversion method, called multi-reflection elimination method, with which the approximate reflectivity fu...
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In this papert we discuss the inverse problem of 1-dimensional acoustic wave equation and propose an approximate inversion method, called multi-reflection elimination method, with which the approximate reflectivity function can be directly obtained by applying a certain transform to the response. The computation efforts for such method is only of the order N log N, much less than that of solving the direct problem, which is O(N2). On the basis of the proposed method, we also construct an iterative algorithm, and prove that the convergent order of iteration is two.
Asynchronous parallel multisplitting nonlinear symmetric Gauss-Seidel methods are established for the system of nonlinear equations , withA, B∈L(Rn) being matrices of particular properties, being diagonal and continu...
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Asynchronous parallel multisplitting nonlinear symmetric Gauss-Seidel methods are established for the system of nonlinear equations , withA, B∈L(Rn) being matrices of particular properties, being diagonal and continuous mappings, and b ∈Rn a known vector. The establishments of these new methods are according to the principle of sufficiently using the delayed information and are concerning about the concrete characteristics of the multiprocessor systems. Therefore, they have considerably higher parallel computingefficiency. The global convergenge as well as the asymptotic convergence rates of these new methods are investigated in detail under suitable conditions.
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