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Hegland, Markus; Anderssen, Robert S.

Dilational interpolatory inequalities. (English) Zbl 1225.65063

Math. Comput. 80, No. 274, 1019-1036 (2011).
The authors propose a new class of Hilbert scales for better error estimates of numerical peak sharpening procedures for solving improperly posed operator equations. Dilational interpolatory inequalities are constructed with one-parameter families of index functions of variable Hilbert scales and dilation of the selected index functions. They contain the ordinary Hilbert scale interpolatory inequalities as special cases. Properties of the proposed interpolatory inequalities and their improvements on the error estimates for peak sharpening deconvolution are discussed.
Relationships to Gaussian, Lorentzian deconvolution are established along with potential application to Voigt and exponential peaks. An analysis of deconvolution peak sharpening is used as an example to illustrate the application of the dilateral interpolatory inequality in deriving approximate error estimates.
It would be more helpful to the numeric community if the paper would be more easily understandable.
Reviewer: Zhen Mei (Toronto)

MSC:

65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
65J15 Numerical solutions to equations with nonlinear operators

Keywords:

Hilbert Scale; error estimates; Index functions; improperly posed operator equations; dilational interpolatory inequalities; peak sharpening deconvolution
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