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For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…

In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their…

In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential…

Repeated application of machine-learning, eigen-centric methods to an evolving dataset reveals that eigenvectors calculated by well-established computer implementations are not stable along an evolving sequence. This is because the sign of…

With only a few exceptions, the numerical simulation of cosmic and laboratory hydromagnetic dynamos has been carried out in the framework of the differential equation method. However, the integral equation method is known to provide robust…

We propose subspace methods for 3-parameter eigenvalue problems. Such problems arise when separation of variables is applied to separable boundary value problems; a particular example is the Helmholtz equation in ellipsoidal and…

Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…

In this paper, we first establish the convergence criteria of the residual iteration method for solving quadratic eigenvalue problem- s. We analyze the impact of shift point and the subspace expansion on the convergence of this method. In…

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…

The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…

We study some aspects of the invariant pair problem for matrix polynomials, as introduced by Betcke and Kressner and by Beyn and Thuemmler. Invariant pairs extend the notion of eigenvalue-eigenvector pairs, providing a counterpart of…

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed…

The performance of eigenvalue problem solvers (eigensolvers) depends on various factors such as preconditioning and eigenvalue distribution. Developing stable and rapidly converging vectorwise eigensolvers is a crucial step in improving the…

Existing image inpainting methods typically fill holes by borrowing information from surrounding pixels. They often produce unsatisfactory results when the holes overlap with or touch foreground objects due to lack of information about the…

This work deals with approximate solution of generalized eigenvalue problem with coefficient matrix that is an affine function of d-parameters. The coefficient matrix is assumed to be symmetric positive definite and spectrally equivalent to…

We review solutions to the problem of depth estimation, arguably the most important subtask in scene understanding. We focus on the single image depth estimation problem. Due to its properties, the single image depth estimation problem is…

Many edge and contour detection algorithms give a soft-value as an output and the final binary map is commonly obtained by applying an optimal threshold. In this paper, we propose a novel method to detect image contours from the extracted…

We propose the algorithm that solves the symmetric cone programs (SCPs) by iteratively calling the projection and rescaling methods the algorithms for solving exceptional cases of SCP. Although our algorithm can solve SCPs by itself, we…

We generalize $\epsilon$-pseudospectra and the associated computational algorithms to the generalized eigenvalue problem. Rank one perturbations are used to determine the $\epsilon$-pseudospectra.

Pole-swapping algorithms, which are generalizations of the QZ algorithm for the generalized eigenvalue problem, are studied. A new modular (and therefore more flexible) convergence theory that applies to all pole-swapping algorithms is…