Inverse spectral analysis for a class of finite band symmetric matrices

@article{Kudryavtsev2014InverseSA,
  title={Inverse spectral analysis for a class of finite band symmetric matrices},
  author={Mikhail Kudryavtsev and Sergio Palafox and Luis O. Silva},
  journal={arXiv: Mathematical Physics},
  year={2014}
}
In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a matrix in our class and give an algorithm for recovering this matrix from the spectral function. The reconstructive algorithm is applicable to matrices which cannot be treated by known inverse block matrix methods. Our approach to the inverse problem is based on… 
1 Citations

Figures from this paper

On a linear interpolation problem for n-dimensional vector polynomials
TLDR
The results of this work generalize previous results on the so-called rational interpolation and have applications to direct and inverse spectral analysis of band matrices.

References

SHOWING 1-10 OF 73 REFERENCES
Rational interpolation and mixed inverse spectral problem for finite CMV matrices
TLDR
The developed technique is applied to give sufficient conditions for the uniqueness of the solution of the mixed inverse spectral problem.
m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices
We study inverse spectral analysis for finite and semi-infinite Jacobi matricesH. Our results include a new proof of the central result of the inverse theory (that the spectral measure determinesH).
An inverse spectral theory for finite CMV matrices
For finite dimensional CMV matrices the classical inverse spectral problems are considered. We solve the inverse problem of reconstructing a CMV matrix by its Weyl's function, the problem of
The numerically stable reconstruction of a Jacobi matrix from spectral data
TLDR
This paper shows how to construct a discrete inner product for which the associated sequence of monic orthogonal polynomials coincides with the sequence of appropriately normalized characteristic polynmials of the left principal submatrices of the Jacobi matrix.
Some Spectral Properties of Infinite Band Matrices
For operators generated by a certain class of infinite band matrices we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying higher order recurrence
On the construction of band matrices from spectral data
Abstract We consider 2m+1 banded Hermitian, skew-Hermitian, or complex-symmetric matrices A. We derive a set of eigenvalues of A and certain of its submatrices whose knowledge enables us to
On the Two Spectra Inverse Problem for Semi-infinite Jacobi Matrices
We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the
The Two-Spectra Inverse Problem for Semi-infinite Jacobi Matrices in The Limit-Circle Case
We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and
Construction of band matrices from spectral data
Abstract A stable numerical algorithm is presented to generate a symmetric p -band matrix from the given eigenvalues of the p greatest leading submatrices. The algorithm consists of two parts. First
On a linear interpolation problem for n-dimensional vector polynomials
TLDR
The results of this work generalize previous results on the so-called rational interpolation and have applications to direct and inverse spectral analysis of band matrices.
...
1
2
3
4
5
...