Related papers: A shifted Laplace rational filter for large-scale …

We give a sufficient condition for branched minimal immersions of spheres into ellipsoids to be embedded: we show that if the coordinate functions of the branched minimal immersion are first or second eigenfunctions with respect to a…

The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…

This paper introduces and analyses the new grid-based tensor approach for approximate solution of the eigenvalue problem for linearized Hartree-Fock equation applied to the 3D lattice-structured and periodic systems. The set of localized…

We suggest a method of construction of general diffeomorphism invariant boundary conditions for metric fluctuations. The case of $d+1$ dimensional Euclidean disk is studied in detail. The eigenvalue problem for the Laplace operator on…

Boundary integral equations and Nystrom discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weakly-singular kernel arises, in which case specialized quadratures that…

In this paper, we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian, we…

The Laplace eigenvalue problem on circular sectors has eigenfunctions with corner singularities. Standard methods may produce suboptimal approximation results. To address this issue, a novel numerical algorithm that enhances standard…

The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…

Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal…

We consider a class of generally non-self-adjoint eigenvalue problems which are nonlinear in the solution as well as in the eigenvalue parameter ("doubly" nonlinear). We prove a bifurcation result from simple isolated eigenvalues of the…

We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…

This paper presents a definition for local linearizations of rational matrices and studies their properties. This definition allows us to introduce matrix pencils associated to a rational matrix that preserve its structure of zeros and…

We consider the application of the WaveHoltz iteration to time-harmonic elastic wave equations with energy conserving boundary conditions. The original WaveHoltz iteration for acoustic Helmholtz problems is a fixed-point iteration that…

The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure…

This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid…

The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…

In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…

We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…

We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…