Estimates of the Accuracy of the Projection Method with a Fractional Smoothness Stabilizer in the Problem of Reconstructing the Wavefront Based on Its Slopes

We consider the projection method with a fractional smoothness stabilizer for approximating the problem of reconstructing the wavefront based on its slopes. The stability of the method is demonstrated on the scale of periodic functions of two arguments. Conditions for matching the stabilizer paramet...

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Bibliographic Details
Published in:Differential equations 2022-07, Vol.58 (7), p.985-998
Main Authors: Razgulin, A. V., Iroshnikov, N. G., Larichev, A. V., Turganbayev, S. A., Romanenko, T. E.
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Differential equations
Estimates
Interpolation
Mathematics
Mathematics and Statistics
Numerical Methods
Ordinary Differential Equations
Partial Differential Equations
Periodic functions
Slope stability
Smoothness
Sobolev space
Wave fronts
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Summary:We consider the projection method with a fractional smoothness stabilizer for approximating the problem of reconstructing the wavefront based on its slopes. The stability of the method is demonstrated on the scale of periodic functions of two arguments. Conditions for matching the stabilizer parameters with the grid step are found; this permits one to derive estimates of the convergence rate of the projection method that are consistent with the smoothness of the slopes. Using interpolation theory, we obtain estimates for the accuracy of the method under natural requirements for the smoothness of slopes from the scale of anisotropic Sobolev spaces of fractional smoothness.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266122070102