Related papers: The infinite bi-Lanczos method for nonlinear eigen…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
Neural networks have revolutionized the field of data science, yielding remarkable solutions in a data-driven manner. For instance, in the field of mathematical imaging, they have surpassed traditional methods based on convex…
Lattice Lipschitz operators define a new class of nonlinear Banach-lattice-valued maps that can be written as diagonal functions with respect to a certain basis. In the $n-$dimensional case, such a map can be represented as a vector of size…
We present two approximation methods for computing eigenfrequencies and eigenmodes of large-scale nonlinear eigenvalue problems resulting from boundary element method (BEM) solutions of some types of acoustic eigenvalue problems in…
We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…
We introduce the concept of mode-k generalized eigenvalues and eigenvectors of a tensor and prove some properties of such eigenpairs. In particular, we derive an upper bound for the number of equivalence classes of generalized tensor…
This paper presents a parallel algorithm for finding the smallest eigenvalue of a particular form of ill-conditioned Hankel matrix, which requires the use of extremely high precision arithmetic. Surprisingly, we find that commonly-used…
We develop numerical algorithms to approximate positive solutions of elliptic boundary value problems with superlinear subcritical nonlinearity on the boundary of the form $-\Delta u + u = 0$ in $\Omega$ with $\frac{\partial u}{\partial…
In this paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in…
We seek to approximate a composite function h(x) = g(f(x)) with a global polynomial. The standard approach chooses points x in the domain of f and computes h(x) at each point, which requires an evaluation of f and an evaluation of g. We…
In this paper, we present a relaxation proximal point method with double inertial effects to approximate a solution of a non-convex equilibrium problem. We give global convergence results of the iterative sequence generated by our…
We provide an algorithm, running in polynomial time in the number of vertices, computing the unique solution to the biased infinity Laplacian Boundary Problem on finite graphs. The algorithm is based on the general outline and approach…
Infinite-dimensional Newton methods can be effectively used to derive numerical proofs of the existence of solutions to partial differential equations (PDEs). In computer-assisted proofs of PDEs, the original problem is transformed into the…
This paper is devoted to the computation of transmission eigenvalues in the inverse acoustic scattering theory. This problem is first reformulated as a two by two boundary system of boundary integral equations. Next, utilizing the Schur…
The distribution of the eigenvalues of a Hermitian matrix (or of a Hermitian matrix pencil) reveals important features of the underlying problem, whether a Hamiltonian system in physics, or a social network in behavioral sciences. However,…
Envelope methods offer targeted dimension reduction for various models. The overarching goal is to improve efficiency in multivariate parameter estimation by projecting the data onto a lower-dimensional subspace known as the envelope.…
We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…
The Lanczos algorithm, introduced by Cornelius Lanczos, has been known for a long time and is widely used in computational physics. While often employed to approximate extreme eigenvalues and eigenvectores of an operator, recently interest…
We propose a characterization of a $p$-Laplace higher eigenvalue based on the inverse iteration method with balancing the Rayleigh quotients of the positive and negative parts of solutions to consecutive $p$-Poisson equations. The approach…
We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…