Related papers: Solving nonlinear eigenvalue problems via contour …
Nonlinear constrained optimization has a wide range of practical applications. In this paper, we consider nonlinear optimization with inequality constraints. The interior point method is considered to be one of the most powerful algorithms…
A detailed new upgrade of the FEAST eigensolver targeting non-Hermitian eigenvalue problems is presented and thoroughly discussed. It aims at broadening the class of eigenproblems that can be addressed within the framework of the FEAST…
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible…
The Boundary Element Method (BEM) is a powerful numerical approach for solving 3D elastostatic problems, particularly useful for crack propagation in fracture mechanics and half-space problems. A key challenge in BEM lies in handling…
This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM…
We investigate new developments of the combined Reduced-Basis and Empirical Interpolation Methods (RB-EIM) for parametrized nonlinear parabolic problems. In many situations, the cost of the EIM in the offline stage turns out to be…
Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches,…
In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…
Nonlinear eigenvalue equations arise naturally in quantum information theory, particularly in the variational quantification of entanglement. In this work, we present a hybrid analytical and numerical framework for evaluating the geometric…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
Over the past years, inverse problems in partial differential equations have garnered increasing interest among scientists and engineers. However, due to the lack of conventional stability, nonlinearity and non-convexity, these problems are…
Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m>>n collocation points. We show how eigenvalue problems can be solved in this…
It is well known that the usual mixed method for solving the biharmonic eigenvalue problem by decomposing the operator into two Laplacians may generate spurious eigenvalues on non-convex domains. To overcome this difficulty, we adopt a…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties…
An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we…
We here investigate the efficient implementation of the energy-conserving methods named Hamiltonian Boundary Value Methods (HBVMs) recently introduced for the numerical solution of Hamiltonian problems. In this note, we describe an…
This paper presents a novel online identification algorithm for nonlinear regression models. The online identification problem is challenging due to the presence of nonlinear structure in the models. Previous works usually ignore the…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…