On stable numerical differentiation (Q2719069)
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scientific article; zbMATH DE number 1597957
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On stable numerical differentiation |
scientific article; zbMATH DE number 1597957 |
Statements
On stable numerical differentiation (English)
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14 May 2001
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numerical differentiation
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noisy data
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ill-posed problems
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multi-point methods
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regularization
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finite difference methods
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algorithms
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Volterra integral equation
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numerical results
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This paper is concerned with a new approach to the construction of finite difference methods for treating the problem of numerical differentiation. It is shown that the multipoint difference schemes may construct stable regularizing algorithms for the process of numerical differentiation with a stepsize \(h\) being a regularization parameter. The construction takes into account that \(h\) must depend on the level of noise of initial data and on the class to which the function to be differentiated belongs. An iterative regularized scheme for solving the problem in the form of a Volterra integral equation is proposed. This procedure is alternative to the variational one and presents some advantages. Interesting numerical results are given and discussed.
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