Inverse eigenvalue problem for bordered diagonal matrices

محورهای موضوعی : Numerical analysis

S. Mashayekhi ¹ , S. M. Karbassi ² , S. A. Shahzadefazeli ³

1 - Department of Mathematics, Faculty of Sciences, Arak University, Arak 38156-8-8349, Iran
2 - Faculty of Mathematics, Yazd University, Yazd, Iran
3 - Faculty of Mathematics, Yazd University, Yazd, Iran

تاریخ دریافت : 1400/06/05 تاریخ پذیرش : 1400/08/23 تاریخ انتشار : 1400/09/10

کلید واژه: Inverse eigenvalue problem, bordered diagonal matrix, leading principal submatrix, minimal eigenvalue, maximal eigenvalue,

چکیده مقاله :

‎In this paper, the inverse eigenvalue problem for the bordered diagonal matrices are reconsidered whose elements are equal to zero except for the first row, the first column and the diagonal elements. The necessary and sufficient conditions for existence of a symmetric bordered diagonal matrix from special spectral data have been determined. A new algorithm to make such matrices is derived and some numerical examples are given to illustrate the efficiency of the method.