scholarly journals Inverse eigenvalue problems for extended Hessenberg and extended tridiagonal matrices

2014 ◽  
Vol 272 ◽  
pp. 377-398 ◽  
Author(s):  
Thomas Mach ◽  
Marc Van Barel ◽  
Raf Vandebril
Keyword(s):  
Eigenvalue Problems ◽  
Tridiagonal Matrices ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue

On inverse eigenvalue problems for two kinds of special banded matrices

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 371-385 ◽  
Author(s):  
Wei-Ru Xu ◽  
Guo-Liang Chen
Keyword(s):  
Eigenvalue Problems ◽  
Sufficient Conditions ◽  
Numerical Algorithms ◽  
Tridiagonal Matrices ◽  
Inverse Eigenvalue Problems ◽  
Banded Matrices ◽  
Inverse Eigenvalue ◽  
Maximal Eigenvalues ◽  
Principal Submatrices ◽  
Necessary And Sufficient

This paper presents two kinds of symmetric tridiagonal plus paw form (hereafter TPPF) matrices, which are the combination of tridiagonal matrices and bordered diagonal matrices. In particular, we exploit the interlacing properties of their eigenvalues. On this basis, the inverse eigenvalue problems for the two kinds of symmetric TPPF matrices are to construct these matrices from the minimal and the maximal eigenvalues of all their leading principal submatrices respectively. The necessary and sufficient conditions for the solvability of the problems are derived. Finally, numerical algorithms and some examples of the results developed here are given.

scholarly journals A Generalized Inexact Newton Method for Inverse Eigenvalue Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Weiping Shen
Keyword(s):  
Newton Method ◽  
Quadratic Convergence ◽  
Eigenvalue Problems ◽  
Generalized Newton Method ◽  
Inexact Newton Method ◽  
Numerical Tests ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue ◽  
Generalized Newton ◽  
Special Case

We propose a generalized inexact Newton method for solving the inverse eigenvalue problems, which includes the generalized Newton method as a special case. Under the nonsingularity assumption of the Jacobian matrices at the solutionc*, a convergence analysis covering both the distinct and multiple eigenvalue cases is provided and the quadratic convergence property is proved. Moreover, numerical tests are given in the last section and comparisons with the generalized Newton method are made.

scholarly journals An inexact Cayley transform method for inverse eigenvalue problems

2004 ◽  
Vol 20 (5) ◽  
pp. 1675-1689 ◽  
Author(s):  
Zheng-Jian Bai ◽  
Raymond H Chan ◽  
Benedetta Morini
Keyword(s):  
Eigenvalue Problems ◽  
Cayley Transform ◽  
Transform Method ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue
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