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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On stable numerical differentiation


Authors: Alexander G. Ramm and Alexandra B. Smirnova
Journal: Math. Comp. 70 (2001), 1131-1153
MSC (2000): Primary 65D25; Secondary 65D05
Published electronically: March 9, 2001
MathSciNet review: 1826578
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Abstract:

A new approach to the construction of finite-difference methods is presented. It is shown how the multi-point differentiators can generate regularizing algorithms with a stepsize $h$ being a regularization parameter. The explicitly computable estimation constants are given. Also an iteratively regularized scheme for solving the numerical differentiation problem in the form of Volterra integral equation is developed.


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Additional Information

Alexander G. Ramm
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506-2602
Email: ramm@math.ksu.edu

Alexandra B. Smirnova
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506-2602
Email: matabs@zeus.cs.gsu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01307-2
PII: S 0025-5718(01)01307-2
Keywords: Numerical differentiation, noisy data, ill-posed problems, multi-point methods, regularization
Received by editor(s): August 5, 1999
Published electronically: March 9, 2001
Article copyright: © Copyright 2001 American Mathematical Society