منابع مشابه
On stable numerical differentiation
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 eq...
متن کاملA Scheme for Stable Numerical Differentiation
A method for stable numerical differentiation of noisy data is proposed. The method requires solving a Volterra integral equation of the second kind. This equation is solved analytically. In the examples considered its solution is computed analytically. Some numerical results of its application are presented. These examples show that the proposed method for stable numerical differentiation is n...
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Practical methods of differentiating a signal known only through its on-line samples are much needed, given the numerous areas in control theory and practice where differentiation is encountered. This communication presents theoretical as well as implementation details on several numerical differentiation algorithms which may be useful in the area of nonlinear estimation. In particular, these a...
متن کاملJ. KSIAM Vol.7, No.1, 47-61, 2003 STABLE NUMERICAL DIFFERENTIATION: WHEN IS IT POSSIBLE?
Two principally different statements of the problem of stable numerical differentiation are considered. It is analyzed when it is possible in principle to get a stable approximation to the derivative f ′ given noisy data fδ. Computational aspects of the problem are discussed and illustrated by examples. These examples show the practical value of the new understanding of the problem of stable di...
متن کاملNumerical Investigation on Stable Crack Growth in Plane Stress
Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension (a/W=0.5) and three-point bend (a/W=0.1 and 0.5) specimens under plane stress condition. The crack growth is controlled by the experimental J-integral resistance curves measured by Sun et al. The results indicate that the distributions of opening st...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2001
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-01-01307-2