Schuster, Thomas; Rieder, Andreas; Schöpfer, Frank The approximate inverse in action. IV: Semi-discrete equations in a Banach space setting. (English) Zbl 1259.65078 Inverse Probl. 28, No. 10, Article ID 104001, 19 p. (2012). The method of approximate inverse is used to solve semi-discrete linear operator equations in Banach spaces as well as to compute scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The authors extend their previous results for convergence and stability to a Banach space setting. Reviewer: R. S. Dahiya (Ames) MSC: 65J10 Numerical solutions to equations with linear operators (do not use 65Fxx) 65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization 47A50 Equations and inequalities involving linear operators, with vector unknowns Keywords:method of approximate inverse; semi-discrete linear operator equations; Banach space; reconstruction kernels; convergence; stability PDF BibTeX XML Cite \textit{T. Schuster} et al., Inverse Probl. 28, No. 10, Article ID 104001, 19 p. (2012; Zbl 1259.65078) Full Text: DOI