Stable approximation of fractional derivatives of rough functions

DOI10.1007/BF01739822zbMath0840.65011MaRDI QIDQ1907870

A. Schneider, Dinh Nho Hào, Hans-Juergen Reinhardt

Publication date: 30 June 1996

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

error estimationwaveletill-posed problemmultiresolution approximationhat functionsmollification methodstep functionsrough functionsnumerical fractional differentiation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Numerical methods for ill-posed problems for integral equations (65R30) Numerical differentiation (65D25)

Related Items (11)

Regularization of ill-posed problems involving constant-coefficient pseudo-differential operators ⋮ Source identification problems for abstract semilinear nonlocal differential equations ⋮ Regularization technique for an inverse space-fractional backward heat conduction problem ⋮ On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor ⋮ Heuristic regularization methods for numerical differentiation ⋮ Hermite spectral and pseudospectral methods for numerical differentiation ⋮ On the ill-posed analytic continuation problem: an order optimal regularization scheme ⋮ Wavelet regularization strategy for the fractional inverse diffusion problem ⋮ A new regularization approach for numerical differentiation ⋮ On optimal regularization methods for fractional differentiation ⋮ An a posteriori wavelet method for solving two kinds of ill-posed problems

Cites Work

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• Abel integral equations. Analysis and applications
• The Grünwald-Letnikov difference operator and regularization of the Weyl fractional differentiation
• A mollification method for ill-posed problems
• Fast wavelet transforms and numerical algorithms I
• Orthonormal bases of compactly supported wavelets
• Ten Lectures on Wavelets
• Stable nunerical fractional differentiation by mollification

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