Sign wave analysis in matrix eigenvalue problems

Sign Wave Analysis in Matrix Eigenvalue Problems

Eigenvalue problems with sign-changing coefficients

We consider a class of eigenvalue problems involving coefficients changing sign on the domain of interest. We describe the main spectral properties of these problems according to the features of the coefficients. Then, under some assumptions on the mesh, we explain how one can use classical finite element methods to approximate the spectrum as well as the eigenfunctions while avoiding spurious ...

Some Unusual Matrix Eigenvalue Problems

We survey some unusual eigenvalue problems arising in different applications. We show that all these problems can be cast as problems of estimating quadratic forms. Numerical algorithms based on the well-known Gauss-type quadrature rules and Lanczos process are reviewed for computing these quadratic forms. These algorithms reference the matrix in question only through a matrix-vector product op...

Eigenvalue Problems in Surface Acoustic Wave Filter Simulations

1 FWF-Start Project Y-192 “3D hp-Finite Elements”, Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria [email protected] 2 Radon Institute for Computational and Applied Mathematics (RICAM), Altenbergerstraße 69, 4040 Linz, Austria [email protected] 3 Institute of Computational Mathematics, Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria ulanger...

A Density Matrix-based Algorithm for Solving Eigenvalue Problems

A new numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques, and takes its inspiration from the contour integration and density matrix representation in quantum mechanics. It will be shown that this new...