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Fathi, Ferya, Fariborzi Araghi, Mohammad Ali, Shahzadeh Fazeli, Seyed Abolfazl. (1401). Inverse spectral problems for arrowhead matrices. فیزیولوژی و بیوتکنولوژی آبزیان, 10(2), 213-225. doi: 10.22124/jmm.2021.19736.1695
Ferya Fathi; Mohammad Ali Fariborzi Araghi; Seyed Abolfazl Shahzadeh Fazeli. "Inverse spectral problems for arrowhead matrices". فیزیولوژی و بیوتکنولوژی آبزیان, 10, 2, 1401, 213-225. doi: 10.22124/jmm.2021.19736.1695
Fathi, Ferya, Fariborzi Araghi, Mohammad Ali, Shahzadeh Fazeli, Seyed Abolfazl. (1401). 'Inverse spectral problems for arrowhead matrices', فیزیولوژی و بیوتکنولوژی آبزیان, 10(2), pp. 213-225. doi: 10.22124/jmm.2021.19736.1695
Fathi, Ferya, Fariborzi Araghi, Mohammad Ali, Shahzadeh Fazeli, Seyed Abolfazl. Inverse spectral problems for arrowhead matrices. فیزیولوژی و بیوتکنولوژی آبزیان, 1401; 10(2): 213-225. doi: 10.22124/jmm.2021.19736.1695

Inverse spectral problems for arrowhead matrices

Journal of Mathematical Modeling
دوره 10، شماره 2، شهریور 2022، صفحه 213-225    اصل مقاله (180 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2021.19736.1695
نویسندگان
Ferya Fathi1؛ Mohammad Ali Fariborzi Araghi* 2؛ Seyed Abolfazl Shahzadeh Fazeli3
1Department of Mathematics, Dezful Branch, Islamic Azad University, Dezful, Iran
2Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
3Department of Computer Science,Yazd University, Yazd, Iran
چکیده
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.
کلیدواژه‌ها
Inverse eigenvalue problem؛ Arrowhead matrix؛ Principal submatrix
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