Approximate solution of large systems of equations with multi–dimensional Toeplitz matrices
Anatoliy Vsevolodovich Kozak, Dmitriy Igorevich Khanin
Southern Federal University, 105/42 Bolshaya Sadovaya Str., Rostov-on-Don, 344006
Keywords: approximate solution, Toeplitz matrices, multi-dimensional cyclic matrices, multi-dimensional convolution operators on polyhedral
Abstract
The conditions using the inverse operator and its form in the truncated two-dimensional convolution operators on sets with smooth boundaries are known. The presence of the corner points adds complexity to the task. The equations with multi-dimensional convolution operators on polyhedra is considered. The approximate method for them is proposed, and estimates for the errors are obtained. The possibility of approximation solutions of these equations with multi-dimensional cyclic matrices is also investigated.
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