The generalized eigenvalue (GE) problems are of particular importance in various areas science engineering and machine learning. We present a variational quantum algorithm for finding the desired GE problem, $\mathcal{A}|\psi\rangle=\lambda\mathcal{B}|\psi\rangle$, by choosing suitable loss functions. Our approach imposes superposition trial state obtained eigenvectors with respect to weighting...

This paper concerns with the sensitivity analysis for the multivariate eigenvalue problem (MEP). The concept of a simple multivariate eigenvalue of a matrix is generalized to the MEP and the first-order perturbation expansions of a simple multivariate eigenvalue and the corresponding multivariate eigenvector are presented. The explicit expressions of condition numbers, perturbation upper bounds...

The generalized eigenvalue problem

We consider variants of Davidson's method for the iterative computation of one or more eigenvalues and their corresponding eigenvectors of an n n matrix A. The original Davidson method 3], for real normal matrices A, may be viewed as an accelerated Gauss-Jacobi method, and the success of the method seems to depend quite heavily on diagonal dominance of A 3, 4, 17]. In the hope to enlarge the sc...

We consider solution of sparse linear systems that arise from generalized eigenvalue problems for molecular orbital calculation of the biochemistry application [2]. This application predicts the reaction and properties of proteins in water molecules through the orbital of molecules indicated by the status of electron distribution. The prediction of the electron distribution requires to obtain a...

The problem of eigenvalue placement via state observer for generalized linear time invariant systems is considered. The main contribute is to whow that even if the well-known Luenberger eigenvalue separation theorem may be easily extended to the generalized case, the solvability of the resulting compensator is not in general assured. It is shown that regularity may be reached by a suitable choi...

This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein’s conic-fitting and Fitzgibbon’s direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem...