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Numerical Analysis and Computation Commons™
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Articles 1 - 4 of 4
Full-Text Articles in Numerical Analysis and Computation
Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N- Dimensions, Kurt Bryan, Lester Caudill
Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N- Dimensions, Kurt Bryan, Lester Caudill
Department of Math & Statistics Faculty Publications
We consider the inverse problem of determining the shape of some inaccessible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivatives, develop methods for regularizing the process, and provide computational examples.
A Posteriori Estimate For Tikhonov Regularization Parameter, S. Abbasbandy
A Posteriori Estimate For Tikhonov Regularization Parameter, S. Abbasbandy
Saeid Abbasbandy
This paper deals the numerical solution of integral equations of the first kind with using regularization method. There are many stopping rules based on discrepancy principle or discussed in [3]. Here a new stopping rule is described which uses SVD (Singular Value Decomposition) and condition number of matrices. Finally, we give a number of numerical examples showing that the method works well in practice.
A Method For Solving Fuzzy Linear Systems, S. Abbasbandy, M. Alavi
A Method For Solving Fuzzy Linear Systems, S. Abbasbandy, M. Alavi
Saeid Abbasbandy
In this paper we present a method for solving fuzzy linear systems by two crisp linear systems. Also necessary and sufficient conditions for existence of solution are given. Some numerical examples illustrate the efficiency of the method.
A New Method For Solving Symmetric Fuzzy Linear Systems, S. Abbasbandy, M. Alavi
A New Method For Solving Symmetric Fuzzy Linear Systems, S. Abbasbandy, M. Alavi
Saeid Abbasbandy
In this paper we represent a new method for solving a symmetric fuzzy linear system by two crisp linear systems. Also necessary and sufficient conditions for the solution existence are given.