Related papers: A degenerate kernel method for eigenvalue problems…

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 consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…

A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a…

We present a finite difference method to compute the principal eigenvalue and the corresponding eigenfunction for a large class of second order elliptic operators including notably linear operators in nondivergence form and fully nonlinear…

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…

It is shown how mixed finite element methods for symmetric positive definite eigenvalue problems related to partial differential operators can provide guaranteed lower eigenvalue bounds. The method is based on a classical compatibility…

This chapter deals with kernel methods as a special class of techniques for surrogate modeling. Kernel methods have proven to be efficient in machine learning, pattern recognition and signal analysis due to their flexibility, excellent…

Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…

In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…

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 this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

We propose two basic assumptions, under which the rate of convergence of the augmented Lagrange method for a class of composite optimization problems is estimated. We analyze the rate of local convergence of the augmented Lagrangian method…

Assume that the eigenvalues of a finite hermitian linear operator have been deduced accurately but the linear operator itself could not be determined with precision. Given a set of eigenvalues $\lambda$ and a hermitian matrix $M$, this…

Kernel matrices are a key quantity in kernel-based approximation, and important properties such as stability and algorithmic convergence can be analyzed with their help. In this work we refine a multivariate Ingham-type theorem, which is…

Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…

The non-local degenerate Cahn-Hilliard equation is derived from the Vlasov equation with long-range attraction. We study the local limit as the delocalization parameter converges to 0. The difficulty arises from the degeneracy which…

Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…

Usually, complex-valued RKHS are presented as an straightforward application of the real-valued case. In this paper we prove that this procedure yields a limited solution for regression. We show that another kernel, here denoted as pseudo…

The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or…