Related papers: Generalized preconditioned locally harmonic residu…
We propose a Preconditioned Locally Harmonic Residual (PLHR) method for computing several interior eigenpairs of a generalized Hermitian eigenvalue problem, without traditional spectral transformations, matrix factorizations, or inversions.…
We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form $T(\lambda)v=0$ that admit a variational characterization of eigenvalues. These problems arise in a variety of applications and are…
Non-Hermitian generalized eigenvalue problems (GEPs) play a significant role in many practical applications, such as mechanical engineering. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for…
This work considers the convergence of GMRES for non-singular problems. GMRES is interpreted as the GCR method which allows for simple proofs of the convergence estimates. Preconditioning and weighted norms within GMRES are considered. The…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
In this study, a \emph{$gH$-subgradient technique} is developed to obtain efficient solutions to the optimization problems with nonsmooth nonlinear convex interval-valued functions. The algorithmic implementation of the developed…
We describe a novel algorithm for solving general parametric (nonlinear) eigenvalue problems. Our method has two steps: first, high-accuracy solutions of non-parametric versions of the problem are gathered at some values of the parameters;…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
In this paper, generalized aspects of least square homotopy perturbations are explored to treat the system of non-linear fractional partial differential equations and the method is called as generalized least square homotopy perturbations…
We propose a verified computation method for partial eigenvalues of a Hermitian generalized eigenproblem. The block Sakurai-Sugiura Hankel method, a contour integral-type eigensolver, can reduce a given eigenproblem into a generalized…
The spectral transformation Lanczos method for the sparse symmetric definite generalized eigenvalue problem for matrices $A$ and $B$ is an iterative method that addresses the case of semidefinite or ill conditioned $B$ using a shifted and…
The use of the Preconditioned Conjugate Gradient (PCG) method for computing the Generalized Least Squares (GLS) estimator of the General Linear Model (GLM) is considered. The GLS estimator is expressed in terms of the solution of an…
Unconditional guaranteed lower and upper eigenvalue bounds are mandatory for the understanding of the Schr\"odinger eigenvalue spectrum and its spectral gaps. While upper eigenvalue bounds are naturally induced by conforming…
While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber agrees with an eigenvalue of the interior Dirichlet problem.…
Many eigenvalue problems arising in practice are often of the generalized form $A\x=\lambda B\x$. One particularly important case is symmetric, namely $A, B$ are Hermitian and $B$ is positive definite. The standard algorithm for solving…
In this research, to solve the large indefinite least squares problem, we firstly transform its normal equation into a sparse block three-by-three linear systems, then use GMRES method with an accelerated preconditioner to solve it. The…
Nonlinear acceleration methods are powerful techniques to speed up fixed-point iterations. However, many acceleration methods require storing a large number of previous iterates and this can become impractical if computational resources are…
Solutions to many partial differential equations satisfy certain bounds or constraints. For example, the density and pressure are positive for equations of fluid dynamics, and in the relativistic case the fluid velocity is upper bounded by…
The convergence of GMRES for solving linear systems can be influenced heavily by the structure of the right hand side. Within the solution of eigenvalue problems via inverse iteration or subspace iteration, the right hand side is generally…
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…