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Your search keyword '"Fariborzi Araghi, Mohammad Ali"' showing total 7 results
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7 results on '"Fariborzi Araghi, Mohammad Ali"'

4. A reliable algorithm to check the accuracy of iterative schemes for solving nonlinear equations: an application of the CESTAC method

Author

Fariborzi Araghi, Mohammad Ali

Abstract

The aim of this study is to apply the discrete stochastic arithmetic (DSA) to validate the class of muli-step iterative methods and find the optimal numerical solution of nonlinear equations. To this end, the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are applied. By using this approach, the optimal number of iteration and the optimal solution with its accuracy are found. In this case, the usual stopping termination in the iterative procedure is replaced by a new criterion which is independent of the given tolerance (ϵ) such that the optimal results are evaluated computationally. A main theorem is proved which shows the accuracy of the iterative schemes by means of the concept of common significant digits. The numerical results are presented to illustrate the efficiency and importance of using the DSA in place of the floating-point arithmetic (FPA).

Published
2024
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7. Inverse spectral problems for arrowhead matrices.

Author

Fathi, Ferya, Fariborzi Araghi, Mohammad Ali, and Shahzadeh Fazeli, Seyed Abolfazl

Subjects
INVERSE problems, NONNEGATIVE matrices, ARROWHEADS, MATRICES (Mathematics), EIGENVALUES, PROBLEM solving
Abstract

The problem of constructing a matrix by its spectral information is called inverse eigenvalue problem (IEP) which arises in a variety of applications. In this paper, we study an IEP for arrowhead matrices in different cases. The problem involves constructing of the matrix by some eigenvalues of each of the leading principal submatrices and one eigenpair. We will also investigate this problem and its variants in the cases of matrix entries being real, nonnegative, positive definite, complex and equal diagonal entries. To solve the problems, a new method to establish a relationship between the IEP and properties of symmetric and general form of matrices is developed. The necessary and sufficient conditions of the solvability of the problems are obtained. Finally, some numerical examples are presented. [ABSTRACT FROM AUTHOR]

Published
2022
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