Sampling and the Eigenvalues of a Quadratic Pencil

2019 ◽  
Vol 18 (1) ◽  
pp. 9-22
Author(s):  
E. Baskaya ◽  
A. Boumenir
Keyword(s):  
Quadratic Pencil

scholarly journals Partial inverse problems for quadratic differential pencils on a graph with a loop

2020 ◽  
Vol 28 (3) ◽  
pp. 449-463 ◽  
Author(s):  
Natalia P. Bondarenko ◽  
Chung-Tsun Shieh
Keyword(s):  
Inverse Problems ◽  
A Priori ◽  
Spectral Characteristics ◽  
The Other ◽  
Boundary Edge ◽  
Partial Inverse ◽  
Quadratic Pencil ◽  
Sturm Liouville ◽  
Differential Pencils ◽  
Liouville Operators

AbstractIn this paper, partial inverse problems for the quadratic pencil of Sturm–Liouville operators on a graph with a loop are studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the loop) from spectral characteristics, while the coefficients on the other edges are known a priori. We obtain uniqueness theorems and constructive solutions for partial inverse problems.

scholarly journals Orthogonality and partial pole assignment for the symmetric definite quadratic pencil

1997 ◽  
Vol 257 ◽  
pp. 29-48 ◽  
Author(s):  
Biswa N. Datta ◽  
Sylvan Elhay ◽  
Yitshak M. Ram
Keyword(s):  
Pole Assignment ◽  
Quadratic Pencil

A CG-Type Method for Inverse Quadratic Eigenvalue Problems in Model Updating of Structural Dynamics

2011 ◽  
Vol 3 (1) ◽  
pp. 65-86
Author(s):  
Jiaofen Li ◽  
Xiyan Hu
Keyword(s):  
Eigenvalue Problem ◽  
Eigenvalue Problems ◽  
Model Updating ◽  
Inverse Eigenvalue Problem ◽  
Computationally Efficient ◽  
Type Method ◽  
Quadratic Pencil ◽  
Model Coefficient ◽  
Inverse Eigenvalue ◽  
The Difference

AbstractIn this paper we first present a CG-type method for inverse eigenvalue problem of constructing real and symmetric matricesM, DandKfor the quadratic pencilQ(λ) =λ2M+ λD+K, so thatQ(λ) has a prescribed subset of eigenvalues and eigenvectors. This method can determine the solvability of the inverse eigenvalue problem automatically. We then consider the least squares model for updating a quadratic pencilQ(λ). More precisely, we update the model coefficient matrices M, C and K so that (i) the updated model reproduces the measured data, (ii) the symmetry of the original model is preserved, and (iii) the difference between the analytical triplet (M, D, K) and the updated triplet (Mnew,Dnew,Knew) is minimized. In this paper a computationally efficient method is provided for such model updating and numerical examples are given to illustrate the effectiveness of the proposed method.

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