Related papers: Reduced basis method for non-symmetric eigenvalue …
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
We present a subspace system identification method based on weighted nuclear norm approximation. The weight matrices used in the nuclear norm minimization are the same weights as used in standard subspace identification methods. We show…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only…
We consider nonlinear eigenvalue problems to compute all eigenvalues in a bounded region on the complex plane. Based on domain decomposition and contour integrals, two robust and scalable parallel multi-step methods are proposed. The first…
The recently developed data-driven eigenmatrix method shows very promising reconstruction accuracy in sparse recovery for a wide range of kernel functions and random sample locations. However, its current implementation can lead to…
In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…
We compare three methods to calculate the nucleon-nucleon t-matrix based on the three-dimensional formulation of J. Golak et al., Phys. Rev. C 81, 034006, (2010). In the first place we solve a system of complex linear inhomogeneous…
In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…
In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate…
In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…
We develop an efficient reduced basis method for the frictional contact problem formulated using Nitsche's method. We focus on the regime of small deformations and on Tresca friction. The key idea ensuring the computational efficiency of…
We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The…
Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
The ADAPT-VQE approach is used to solve the neutron-proton pairing problem in atomic nuclei. This variational approach is considered today as one of the most powerful methods to iteratively find the ground state of a many-body problem,…
We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…