TY - JOUR
ID - 5010
TI - Inverse spectral problems for arrowhead matrices
JO - Journal of Mathematical Modeling
JA - JMM
LA - en
SN - 2345-394X
AU - Fathi, Ferya
AU - Fariborzi Araghi, Mohammad Ali
AU - Shahzadeh Fazeli, Seyed Abolfazl
AD - Department of Mathematics, Dezful Branch, Islamic Azad University, Dezful, Iran
AD - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
AD - Department of Computer Science,Yazd University, Yazd, Iran
Y1 - 2022
PY - 2022
VL - 10
IS - 2
SP - 213
EP - 225
KW - Inverse eigenvalue problem
KW - Arrowhead matrix
KW - Principal submatrix
DO - 10.22124/jmm.2021.19736.1695
N2 - 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.
UR - https://jmm.guilan.ac.ir/article_5010.html
L1 - https://jmm.guilan.ac.ir/article_5010_61a4d98f5207693ce479fd614d0102dc.pdf
ER -