Related papers: Fast eigenpairs computation with operator adapted …
We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought…
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…
Methods for the computation of classical Gaussian quadrature rules are described which are effective both for small and large degree. These methods are reliable because the iterative computation of the nodes has guaranteed convergence, and…
We present a rational filter for computing all eigenvalues of a symmetric definite eigenvalue problem lying in an interval on the real axis. The linear systems arising from the filter embedded in the subspace iteration framework, are solved…
Single-reference methods such as Hartree-Fock-based coupled cluster theory are well known for their accuracy and efficiency for weakly correlated systems. For strongly correlated systems, more sophisticated methods are needed. Recent…
We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of…
We leverage the proximal Galerkin algorithm (Keith and Surowiec, Foundations of Computational Mathematics, 2024, DOI: 10.1007/s10208-024-09681-8), a recently introduced mesh-independent algorithm, to obtain a high-order finite element…
We present a fast, adaptive multiresolution algorithm for applying integral operators with a wide class of radially symmetric kernels in dimensions one, two and three. This algorithm is made efficient by the use of separated representations…
This paper presents a Jacobi-type iteration for computing a given specified eigenpair of a symmetric matrix. For a certain class of diagonally dominant matrices, the procedure is shown to converge at a linear rate depending on how the…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
We develop a formalism to compute the statistics of the top eigenpair of weighted sparse graphs with finite mean connectivity and bounded maximal degree. Framing the problem in terms of optimisation of a quadratic form on the sphere and…
In this paper, we develop new fast and efficient algorithms for designing single/multiple unimodular waveforms/codes with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and…
We describe a fast, direct solver for elliptic partial differential equations on a two-dimensional hierarchy of adaptively refined, Cartesian meshes. Our solver, inspired by the Hierarchical Poincar\'e-Steklov (HPS) method introduced by…
The paper suggests a preconditioning type method for fast solving of elliptic equations with oscillating quasiperiodic coefficients $A_\epsilon$ specified by the small parameter $\epsilon>0$. We use an iteration method generated by an…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
We apply the local discontinuous Galerkin (LDG for short) method to solve a mixed boundary value problems for the Helmholtz equation in bounded polygonal domain in 2D. Under some assumptions on regularity of the solution of an adjoint…
How close are Galerkin eigenvectors to the best approximation available out of the trial subspace ? Under a variety of conditions the Galerkin method gives an approximate eigenvector that approaches asymptotically the projection of the…
Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tremendous successes in the areas of signal/image processing…
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…
We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number $\kappa$ in bounded domains in $\mathbb{R}^d$. The discrete trial and test spaces are generated from…