For generalized eigenvalue problems, we consider computing all eigenvalues located in a certain region and their corresponding eigenvectors. Recently, contour integral spectral projection methods have been proposed for such problems. In this study, from an analysis of the relationship between the contour integral spectral projection and the Krylov subspace, we provide a novel interpretation of ...

A generalization of the the flat extension theorems of Curto and Fialkow and Laurent and Mourrain is obtained by seeing the problem as one of ideal projection. Some other results on ideal projection are generalized, and it is seen that a linear functional on the k-variate polynomials over C is finitely atomic if and only if its moment matrix has finite rank, a fact previously known for positive...

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...

In a real uniformly convex and uniformly smooth Banach space, some new monotone projection iterative algorithms for countable maximal monotone mappings and countable weakly relatively non-expansive mappings are presented. Under mild assumptions, some strong convergence theorems are obtained. Compared to corresponding previous work, a new projection set involves projection instead of generalized...

We propose a new projection algorithm for solving the variational inequality problem, where the underlying function is continuous and satisfies a certain generalized monotonicity assumption (e.g., it can be pseudomonotone). The method is simple and admits a nice geometric interpretation. It consists of two steps. First, we construct an appropriate hyperplane which strictly separates the current...

In this paper, we consider a new algorithm for a generalized system for relaxed cocoercive nonlinear inequalities in Hilbert spaces by the convergence of projection methods. Our results extend and improve the recent ones announced by many others.

In this paper, we are concerned with the computation of a few eigenpairs with smallest eigenvalues in absolute value of quadratic eigenvalue problems. We first develop a semiorthogonal generalized Arnoldi method where the name comes from the application of a pseudo inner product in the construction of a generalized Arnoldi reduction [25] for a generalized eigenvalue problem. The method applies ...