相关论文: Verified partial eigenvalue computations using con…
An efficient Jacobi-Galerkin spectral method for calculating eigenvalues of Riesz fractional partial differential equations with homogeneous Dirichlet boundary values is proposed in this paper. In order to retain the symmetry and positive…
Preconditioned iterative methods for numerical solution of large matrix eigenvalue problems are increasingly gaining importance in various application areas, ranging from material sciences to data mining. Some of them, e.g., those using…
In this article we derive a priori error estimates for the $hp$-version of the mortar finite element method for parabolic initial-boundary value problems. Both semidiscrete and fully discrete methods are analysed in $L^2$- and $H^1$-norms.…
In this paper, we introduce a fast Fourier-Galerkin method for solving boundary integral equations on torus-shaped surfaces, which are diffeomorphic to a torus. We analyze the properties of the integral operator's kernel to derive the decay…
The radii polynomial approach is an a posteriori validation method based on the contraction of a quasi-Newton operator. We apply this strategy to give a computer-assisted proof of a transverse heteroclinic orbit in the Shimizu--Morioka…
We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order $\alpha\in (3/2,2)$ on the unit interval $(0,1)$. The standard Galerkin finite element approximation converges slowly due to the presence of…
We present selected examples demonstrating an alternative approach to contour deformation for numerically computing loop integrals in the Minkowski regime. This method focuses on identifying singular hypersurfaces (varieties of the…
In this paper, based on the two-step discretization scheme proposed by Dahlquist, Liniger and Nevanlinna (DLN), we develop a semi-implicit Galerkin finite element method for solving the coupled generalized Ginzburg-Landau equations. By…
Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for…
In this paper, a new type of multi-level correction scheme is proposed for solving eigenvalue problems by finite element method. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which…
The Hankel-norm approximation is a model reduction method which provides the best approximation in the Hankel semi-norm. In this paper the computation of the optimal Hankel-norm approximation is generalized to the case of linear…
We present a randomized, inverse-free algorithm for producing an approximate diagonalization of any $n \times n$ matrix pencil $(A,B)$. The bulk of the algorithm rests on a randomized divide-and-conquer eigensolver for the generalized…
We propose a method for the treatment of two--point boundary value problems given by nonlinear ordinary differential equations. The approach leads to sequences of roots of Hankel determinants that converge rapidly towards the unknown…
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…
Convex (specifically semidefinite) relaxation provides a powerful approach to constructing robust machine perception systems, enabling the recovery of certifiably globally optimal solutions of challenging estimation problems in many…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…
In this paper, we present a protocol for computing the principal eigenvector of a collection of data matrices belonging to multiple semi-honest parties with privacy constraints. Our proposed protocol is based on secure multi-party…
We present Gerschgorin-type eigenvalue inclusion sets applicable to generalized eigenvalue problems.Our sets are defined by circles in the complex plane in the standard Euclidean metric, and are easier to compute than known similar…
Pricing exotic multi-asset path-dependent options requires extensive Monte Carlo simulations. In the recent years the interest to the Quasi-monte Carlo technique has been renewed and several results have been proposed in order to improve…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…