Two new regularization algorithms for solving the first-kind Volterra integral equation, which describes the pressure-rate deconvolution problem in well test data interpretation, are developed in this paper. The main ...Two new regularization algorithms for solving the first-kind Volterra integral equation, which describes the pressure-rate deconvolution problem in well test data interpretation, are developed in this paper. The main features of the problem are the strong nonuniform scale of the solution and large errors (up to 15%) in the input data. In both algorithms, the solution is represented as decomposition on special basic functions, which satisfy given a priori information on solution, and this idea allow us significantly to improve the quality of approximate solution and simplify solving the minimization problem. The theoretical details of the algorithms, as well as the results of numerical experiments for proving robustness of the algorithms, are presented.展开更多
Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di- mensional absolute retracts. Michigan Math. J., 33, 291-313 （1986）] on strong Z-sets in ANR＇s and absorbing sets is generaliz...Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di- mensional absolute retracts. Michigan Math. J., 33, 291-313 （1986）] on strong Z-sets in ANR＇s and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w（U） ---- w（X） （where ＂w＂is the topological weight） for each open nonempty subset U of X, then X itself i,~ homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever X is an AR, its weak product W（X, ＊） ---- {（xn）=l C X ： x~ = ＊ for almost all n} is homeomorphic to a pre-Hilbert space E with E EE. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.展开更多
文摘Two new regularization algorithms for solving the first-kind Volterra integral equation, which describes the pressure-rate deconvolution problem in well test data interpretation, are developed in this paper. The main features of the problem are the strong nonuniform scale of the solution and large errors (up to 15%) in the input data. In both algorithms, the solution is represented as decomposition on special basic functions, which satisfy given a priori information on solution, and this idea allow us significantly to improve the quality of approximate solution and simplify solving the minimization problem. The theoretical details of the algorithms, as well as the results of numerical experiments for proving robustness of the algorithms, are presented.
文摘Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di- mensional absolute retracts. Michigan Math. J., 33, 291-313 （1986）] on strong Z-sets in ANR＇s and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w（U） ---- w（X） （where ＂w＂is the topological weight） for each open nonempty subset U of X, then X itself i,~ homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever X is an AR, its weak product W（X, ＊） ---- {（xn）=l C X ： x~ = ＊ for almost all n} is homeomorphic to a pre-Hilbert space E with E EE. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.
