Approximation theory

Daghestan Electronic Mathematical Reports: Issue 14 (2020)

Reconstruction of a second rank tensor field with zero trace from incomplete data

Medzhidov Ziyaudin Gadzhievich

UDK: 517.4

Pages: 38 - 47

DOI: 10.31029/demr.14.4


An algorithm for the complete reconstruction of a tensor field of rank 2 in three-dimensional Euclidean space on incomplete integral data is constructed. The solenoid part of the field is constructed using linear integrals on straight lines that intersect a curve at infinity, and the displacement field is constructed using the traceless normal ray integrals.


Keywords: ray transform, second-rank tensor field, reconstruction, Saint-Venant operator, displacement field, traceless normal part.




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