相关论文: Inverse eigenvalue problem for discrete three-diag…
We give a short review of results on inverse spectral problems for ordinary differential operators on a spatial networks (geometrical graphs). We pay the main attention to the most important nonlinear inverse problems of recovering…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…
Adapting the method of Andrews-Clutterbuck we prove an eigenvalue gap theorem for a class of non symmetric second order linear elliptic operators on a convex domain in euclidean space. The class of operators includes the Bakry-Emery…
In this study, the theorem on necessary and sufficient conditions for the solvability of inverse problem for Sturm-Liouville operator with discontinuous coefficient is proved and the algorithm of reconstruction of potential from spectral…
We study the Dirichlet problem for the weighted Schr\"odinger operator \[-\Delta u +Vu = \lambda \rho u,\] where $\rho$ is a positive weighting function and $V$ is a potential. Such equations appear naturally in conformal geometry and in…
The matrix Numerov method provides an efficient framework for solving the time-independent Schr\"odinger equation as a matrix eigenvalue problem. However, for singular potentials such as the Coulomb interaction, the expected fourth-order…
In this paper, we propose a new finite element approach, which is different than the classic Babuska-Osborn theory, to approximate Dirichlet eigenvalues. The Dirichlet eigenvalue problem is formulated as the eigenvalue problem of a…
This paper is devoted to the computation of transmission eigenvalues in the inverse acoustic scattering theory. This problem is first reformulated as a two by two boundary system of boundary integral equations. Next, utilizing the Schur…
The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with…
To provide mathematically rigorous eigenvalue bounds for the Steklov eigenvalue problem, an enhanced version of the eigenvalue estimation algorithm developed by the third author is proposed, which removes the requirements of the positive…
We consider a second order functional-differential pencil with two constant delays of the argument and study the inverse problem of recovering its coefficients from the spectra of two boundary value problems with one common boundary…
We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with…
This paper proposes and analyzes a new weak Galerkin method for the eigenvalue problem by using the shifted-inverse power technique. A high order lower bound can be obtained at a relatively low cost via the proposed method. The error…
We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and…
The purpose of this paper is twofold: firstly, we present a new type of relationship between inverse problems and nonlinear differential equations. Secondly, we introduce a new type of inverse spectral problem, posed as follows: for a…
A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete…
Inverse scattering problem for the operator representing sum of the operator of the third derivative on semi-axis and of the operator of multiplication by a real function is studied in this paper. Properties of Jost solutions of such an…
The problem of computing recurrence coefficients of sequences of rational functions orthogonal with respect to a discrete inner product is formulated as an inverse eigenvalue problem for a pencil of Hessenberg matrices. Two procedures are…
The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…
We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…