We first develop an efficient spectral-Galerkin method and an rigorous error analysis for the generalized eigenvalue problems associated to a transmission eigenvalue problem. Then, we present an iterative scheme, based on computation of the first transmission eigenvalue, to estimate the index of refraction of an inhomogeneous medium. We present ample numerical results to demonstrate the effecti...

A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient conditions for the existence of transmission eigenvalues and completeness of generalized eigenstates for the transmission eigenvalue problem are derived. In the trac...

Many problems require the selection of a subset variables from full set optimization variables. The computational complexity an exhaustive search over all possible subsets is, however, prohibitively expensive, necessitating more efficient but potentially suboptimal strategies. We focus on sparse variable for generalized Rayleigh quotient and eigenvalue problems. Such often arise in signal proce...

We study spectral properties of Dirac operators on bounded domains $$\Omega \subset {\mathbb {R}}^3$$ with boundary conditions electrostatic and Lorentz scalar type which depend a parameter $$\tau \in \mathbb {R}$$ ; the case = 0$$ corresponds to MIT bag model. show that eigenvalues are parametrized as increasing functions $$ , we exploit this monotonicity limits \rightarrow \pm \infty . prove ...