The quadratic inverse eigenvalue problem (QIEP) is to find the three matrices M,C, and K, given a set of numbers, closed under complex conjugations, such that these numbers become the eigenvalues of the quadratic pencil P (λ) = λM + λC + K. The affine inverse quadratic eigenvalue problem (AQIEP) is the QIEP with an additional constraint that the coefficient matrices belong to an affine family, ...

In this literature, the symmetric inverse generalized eigenvalue problem with submatrix constraints and its corresponding optimal approximation problem are studied. A necessary and sufficient condition for solvability is derived, and when solvable, the general solutions are presented.

The author studies the inverse scattering problem for a boundary value problem of a generalized one dimensional Schrödinger type with a discontinuous coefficient and eigenparameter dependent boundary condition. The solutions of the considered eigenvalue equation is presented and its scattering function that satisfies some properties is induced. The discrete spectrum is studied and the resolvent...

Iterative methods for inverse eigenvalue problems involve simultaneous approximation of the matrix being sought and its eigenvectors This paper revisits one such method for the inverse Toeplitz eigenvalue problems by exploring the eigenstructure of centrosymmetric matrices All itera tions are now taking place on a much smaller subspace One immediate consequence is that the size of the problem i...

The necessary condition for eigenvalue values of a circulant matrix is studied It is then proved that the necessary condition also su ces the existence of a circulant matrix with the prescribed eigenvalue values Introduction An n n matrix C of the form C c c cn cn c c cn cn cn c cn c c cn c is called a circulant matrix As each row of a circulant matrix is just the previous row cycled forward on...

X iv :m at h/ 05 05 09 5v 1 [ m at h. R A ] 5 M ay 2 00 5 The inverse eigenvalue problem for symmetric anti-bidiagonal matrices Olga Holtz Department of Mathematics University of California Berkeley, California 94720 USA March 6, 2008

We first give the representation of the general solution of the following inverse quadratic eigenvalue problem IQEP : given Λ diag{λ1, . . . , λp} ∈ Cp×p , X x1, . . . , xp ∈ Cn×p, and both Λ and X are closed under complex conjugation in the sense that λ2j λ2j−1 ∈ C, x2j x2j−1 ∈ C for j 1, . . . , l, and λk ∈ R, xk ∈ R for k 2l 1, . . . , p, find real-valued symmetric 2r 1 -diagonal matrices M,...

We consider the following inverse eigenvalue problem: to construct a symmetrical tridiagonal matrix from the minimal and maximal eigenvalues of all its leading principal submatrices. We give a necessary and sufficient condition for the existence of such a matrix and for the existence of a nonnegative symmetrical tridiagonal matrix. Our results are constructive, in the sense that they generate a...

A B€acklund transformation both in bilinear form and in ordinary form for the transformed Vakhnenko equation is derived. An inverse scattering problem is formulated. The inverse scattering method has a third-order eigenvalue problem. A procedure for finding the exact N -soliton solution of the Vakhnenko equation via the inverse scattering method is described. The procedure is illustrated by con...