Related papers: A New Subspace Iteration Algorithm for Solving Gen…

For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…

We present a Chebyshev collocation method for linear ODE and DDE problems. We first give a posteriori estimates for the accuracy of the approximate solution of a scalar ODE initial value problem. Examples of the success of the estimate are…

Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…

The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…

Deep neural networks are powerful tools for approximating functions, and they are applied to successfully solve various problems in many fields. In this paper, we propose a neural network-based numerical method to solve partial differential…

Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…

We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigenvalue problem posed in a polygonal domain. The algorithm is…

In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…

We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…

Approximating adequate number of clusters in multidimensional data is an open area of research, given a level of compromise made on the quality of acceptable results. The manuscript addresses the issue by formulating a transductive…

In this paper, a new framework for continuous-time maximum a posteriori estimation based on the Chebyshev polynomial optimization (ChevOpt) is proposed, which transforms the nonlinear continuous-time state estimation into a problem of…

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…

Bayesian optimization is widely employed for optimizing complex black-box functions but struggles with the curse of dimensionality. Random embedding, as a dimension reduction strategy, simplifies tasks that possess the effective dimension…

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…

The Sparse Generalized Eigenvalue Problem (sGEP), a pervasive challenge in statistical learning methods including sparse principal component analysis, sparse Fisher's discriminant analysis, and sparse canonical correlation analysis,…

A Fourier-Chebyshev spectral method is proposed in this paper for solving the cavitation problem in nonlinear elasticity. The interpolation error for the cavitation solution is analyzed, the elastic energy error estimate for the discrete…

In this paper, a full (nested) multigrid scheme is proposed to solve eigenvalue problems. The idea here is to use the multilevel correction method to transform the solution of eigenvalue problem to a series of solutions of the corresponding…

Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss-Seidel iterative solution of linear equations in the precision matrix. Specifically, the…

Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass…

Efficient simulation of nonlinear and dispersive free-surface flows governed by the incompressible Navier-Stokes equations remains a central challenge in ocean and coastal engineering. The computational bottleneck arises from solving a…