Related papers: A fast iterative algorithm for near-diagonal eigen…
Graph pattern matching algorithms to handle million-scale dynamic graphs are widely used in many applications such as social network analytics and suspicious transaction detections from financial networks. On the other hand, the computation…
The application of eigenvalue theory to dual quaternion Hermitian matrices holds significance in the realm of multi-agent formation control. In this paper, we study the Rayleigh quotient iteration (RQI) for solving the right eigenpairs of…
We present a code for solving the single-particle, time-independent Schr\"odinger equation in two dimensions. Our program utilizes the imaginary time propagation (ITP) algorithm, and it includes the most recent developments in the ITP…
Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integration. One remedy is to integrate in a parallel fashion,…
In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the induced primal-dual regularization, the authors propose to…
In this paper we discuss an abstract iteration scheme for the calculation of the smallest eigenvalue of an elliptic operator eigenvalue problem. A short and geometric proof based on the preconditioned inverse iteration (PINVIT) for matrices…
Basing on a modification of the "Dichotomy Algorithm" (Terekhov, 2010), we propose a parallel procedure for solving tridiagonal systems of equations with Toeplitz matrices. Taking the structure of the Toeplitz matrices, we may substantially…
This paper presents a new algorithm for the parallel in time (PiT) numerical simulation of time dependent partial/ordinary differential equations. We propose a reliable alternative to the well know parareal in time algorithm, by formulating…
A new iterative method for solving large scale symmetric nonlinear eigenvalue problems is presented. We firstly derive an infinite dimensional symmetric linearization of the nonlinear eigenvalue problem, then we apply the indefinite Lanczos…
We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…
We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…
In one of the most important methods in Density Functional Theory - the Full-Potential Linearized Augmented Plane Wave (FLAPW) method - dense generalized eigenproblems are organized in long sequences. Moreover each eigenproblem is strongly…
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…
In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Determining the steady state of an open quantum system is crucial for characterizing quantum devices and studying various physical phenomena. Often, computing a single steady state is insufficient, and it is necessary to explore its…
Matrix and tensor completion aim to recover a low-rank matrix / tensor from limited observations and have been commonly used in applications such as recommender systems and multi-relational data mining. A state-of-the-art matrix completion…
Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…
In this article we consider the inversion problem for polynomially computable discrete functions. These functions describe behavior of many discrete systems and are used in model checking, hardware verification, cryptanalysis, computer…
This paper proposes and analyzes an a posteriori error estimator for the finite element multi-scale discretization approximation of the Steklov eigenvalue problem. Based on the a posteriori error estimates, an adaptive algorithm of shifted…