Related papers: A mixed precision preconditioned Jacobi method for…
We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of…
We propose and analyze a finite element method for the Oseen eigenvalue problem. This problem is an extension of the Stokes eigenvalue problem, where the presence of the convective term leads to a non-symmetric problem and hence, to complex…
This paper proposes and analyzes an a posteriori error estimator for the finite element multi-scale discretization approximation of the Steklov eigenvalue problem. Based on the a posteriori error estimates, an adaptive algorithm of shifted…
In this paper a recursive algorithm is presented for evaluating multivariate Pad\'e approximants (of the rectangular type described in the work of Lutterodt) which is analogous to the Jacobi formula for univariate Pad\'e approximants. This…
In applications of linear algebra including nuclear physics and structural dynamics, there is a need to deal with uncertainty in the matrices. We focus on matrices that depend on a set of parameters $\omega$ and we are interested in the…
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the…
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;…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
This note shows how to compute, to high relative accuracy under mild assumptions, complex Jacobi rotations for diagonalization of Hermitian matrices of order two, using the correctly rounded functions $\mathtt{cr\_hypot}$ and…
In this work, a new algorithm for solving symmetric indefinite systems of linear equations is presented. It factorizes the matrix into the form LDLt using Jacobi rotations in order to increase the pivot's absolute value. Furthermore, Rook's…
We present a hierarchically blocked one-sided Jacobi algorithm for the singular value decomposition (SVD), targeting both single and multiple graphics processing units (GPUs). The blocking structure reflects the levels of GPU's memory…
It was recently demonstrated that the boundary element method based on the Burton-Miller formulation (BM-BEM), widely used for solving exterior problems, can be adapted to solve transmission problems efficiently. This approach utilises…
A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by smoothing steps on a series of multilevel finite…
In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…
The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low order schemes iteratively to produce a high order…
We describe preconditioned iterative methods for estimating the number of eigenvalues of a Hermitian matrix within a given interval. Such estimation is useful in a number of applications.In particular, it can be used to develop an efficient…
Subspace methods are commonly used for finding approximate eigenvalues and singular values of large-scale matrices. Once a subspace is found, the Rayleigh-Ritz method (for symmetric eigenvalue problems) and Petrov-Galerkin projection (for…
In this work we are interested in general linear inverse problems where the corresponding forward problem is solved iteratively using fixed point methods. Then one-shot methods, which iterate at the same time on the forward problem solution…
This paper considers the finite element solution of the boundary value problem of Poisson's equation and proposes a guaranteed em a posteriori local error estimation based on the hypercircle method. Compared to the existing literature on…
Two asymptotically exact a posteriori error estimates are proposed for eigenvalues by the nonconforming Crouzeix--Raviart and enriched Crouzeix-- Raviart elements. The main challenge in the design of such error estimators comes from the…