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- W2130714525 abstract "This article concerns the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search for a solution in an infinite-dimensional Banach space having only a finite number of data available. In this sense the situation is applicable to a large variety of applications where a measurement process delivers a discretization of an infinite-dimensional data space. The method of approximate inverse computes scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The convergence, approximation power and regularization property of this method when applied to semi-discrete operator equations in Hilbert spaces has been investigated in three prequels to this paper. Here we extend these results to a Banach space setting. We prove convergence and stability for general Banach spaces and reproduce the results specifically for the integration operator acting on the space of continuous functions." @default.
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- W2130714525 date "2012-10-01" @default.
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- W2130714525 title "The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting" @default.
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- W2130714525 doi "https://doi.org/10.1088/0266-5611/28/10/104001" @default.
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