Numerical Differentiation as an Example for Inverse Problems
نویسنده
چکیده
We present an error analysis for the numerical diierentiation of noisy data via smoothing cubic splines. Our treatment is elementary enough to be included in a course on numerical analysis. Still, it accounts for all numerical problems that arise in the solution of much more complex ill-posed inverse problems.
منابع مشابه
Implementation of Sinc-Galerkin on Parabolic Inverse problem with unknown boundary condition
The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $...
متن کاملMathematical Modeling and Numerical Investigation of Heat Flux at the External Surface of Cylinder of an Internal Combustion Engine
Abstract: This study deals with modeling of heat flux at the external surface of combustion chamber wall in an internal combustion (IC) engine as a function of crank angle. This investigation results in an inverse heat conduction problem in the cylinder wall. Alifanov regularization method is used for solving this inverse problem. This problem study as an optimization problem in which a square...
متن کاملA numerical Algorithm Based on Chebyshev Polynomials for Solving some Inverse Source Problems
In this paper, two inverse problems of determining an unknown source term in a parabolic equation are considered. First, the unknown source term is estimated in the form of a combination of Chebyshev functions. Then, a numerical algorithm based on Chebyshev polynomials is presented for obtaining the solution of the problem. For solving the problem, the operational matrices of int...
متن کاملMerging DMUs Based on of the idea Inverse DEA
In this paper, we propose a novel method using multiple-objective programming problems to answer the following question: if among a group of decision making units (DMUs), a subset of DMUs are required to merge and form a new DMU with specific input/output levels and a predefined efficiency target, how much should be the outputs/inputs of the merged DMU? This question answered according to the c...
متن کاملA novel computational procedure based on league championship algorithm for solving an inverse heat conduction problem
Inverse heat conduction problems, which are one of the most important groups of problems, are often ill-posed and complicated problems, and their optimization process has lots of local extrema. This paper provides a novel computational procedure based on finite differences method and league championship algorithm to solve a one-dimensional inverse heat conduction problem. At the beginning, we u...
متن کامل