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On stable numerical differentiation |
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| Authors: | Alexander G Ramm Alexandra B Smirnova |
| Affiliation: | Department of Mathematics, Kansas State University, Manhattan, Kansas 66506-2602 ; Department of Mathematics, Kansas State University, Manhattan, Kansas 66506-2602 |
| 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 |
| Keywords: | Numerical differentiation noisy data ill-posed problems multi-point methods regularization |
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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. 