Related papers: A numerical projection technique for large-scale e…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
We propose a black-box approach to reducing large semidefinite programs to a set of smaller semidefinite programs by projecting to random linear subspaces. We evaluate our method on a set of polynomial optimization problems, demonstrating…
We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex…
Quantum dynamics can be analyzed via the structure of energy eigenstates. However, in the many-body setting, preparing eigenstates associated with finite temperatures requires time scaling exponentially with system size. In this work we…
The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take…
Quantum computing offers several new pathways toward finding many-body eigenstates, with variational approaches being some of the most flexible and near-term oriented. These require particular parameterizations of the state, and for solving…
This article deals with the efficient and certified numerical approximation of the smallest eigenvalue and the associated eigenspace of a large-scale parametric Hermitian matrix. For this aim, we rely on projection-based model order…
We develop a rigorous system-agnostic method to predict quantum thermalization in an overwhelming fraction of accessible pure states in a many-body system, entirely in terms of certain out-of-time-ordered correlators of few-body…
Recent advances in both theoretical and computational methods have enabled large-scale, precision calculations of the properties of atomic nuclei. With the growing complexity of modern nuclear theory, however, also comes the need for novel…
This note considers the multidimensional unstructured sparse recovery problems. Examples include Fourier inversion and sparse deconvolution. The eigenmatrix is a data-driven construction with desired approximate eigenvalues and eigenvectors…
An improved hyperspherical harmonic method for the quantum three-body problem is presented to separate three rotational degrees of freedom completely from the internal ones. In this method, the Schr\"{o}dinger equation of three-body problem…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
This note considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. The main challenges are…
This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finite-difference or finite-element formulations. The relationship of real-space approaches to linear-scaling…
In this note we approach the classical, Newtonian, gravitational $N$-body problem by mean of a new, original numerical integration method. After a short summary of the fundamental characteristics of the problem, including a sketch of some…
The recent literature on first order methods for smooth optimization shows that significant improvements on the practical convergence behaviour can be achieved with variable stepsize and scaling for the gradient, making this class of…
Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e. solving minimal…
We consider the problem of projecting a vector onto the so-called k-capped simplex, which is a hyper-cube cut by a hyperplane. For an n-dimensional input vector with bounded elements, we found that a simple algorithm based on Newton's…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…