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Appl Math (Prague) 2021 19;66(6):813-814. Epub 2021 Nov 19.

Department of Mathematics, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Praha 6, Czech Republic.

Appl Math (Prague) 2021 Aug 14:1-29. Epub 2021 Aug 14.

Department of Mathematics, National Institute of Technology, Great Eastern Rd, Raipur, Chhattisgarh, 492001 India.

Recently, Wang (2017) has introduced the -nonnegative double splitting using the notion of matrices that leave a cone K ⊆ ℝ invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for -weak regular and -nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory for these sub-classes of matrices. Read More

Appl Math (Prague) 2011 Dec;56(6):533-541

Denver, CO, USA.

Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and bounds on the ensemble then give convergence. Read More