Related papers: Fast methods for computing the Neuberger Operator
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…
The article presents a matrix differential operator and a pseudoinverse matrix differential operator for finding a particular solution to nonhomogeneous linear ordinary differential equations (ODE) with constant coefficients with special…
In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…
We discuss approaches to computing eigenfunctions of the Ornstein--Uhlenbeck (OU) operator in more than two dimensions. While the spectrum of the OU operator and theoretical properties of its eigenfunctions have been well characterized in…
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of…
We construct a Neural Network that approximates the matrix multiplication operator for any activation function such that there exists a Neural Network which can approximate the scalar multiplication function. In particular, we use the…
We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of increasing operator complexity. Guided by the AMG theory on…
Improved algorithms for computing (partial and full) exterior algebraic shifts of hypergraphs and simplicial complexes are presented. The main benefit is in positive characteristic. Experiments with an implementation in OSCAR with various…
In this paper, we propose an algorithm combining the forward-backward splitting method and the alternative projection method for solving the system of splitting inclusion problem. We want to find a point in the interception of a finite…
Efficient and fast predictor-corrector methods are proposed to deal with nonlinear Caputo-Fabrizio fractional differential equations, where Caputo-Fabrizio operator is a new proposed fractional derivative with a smooth kernel. The proposed…
We consider the use of rational basis functions to compute the scattering and inverse scattering transforms associated with the AKNS system. The proposed numerical forward scattering transform computes the solution of the AKNS system that…
For matrices with displacement structure, basic operations like multiplication, inversion, and linear system solving can all be expressed in terms of the following task: evaluate the product $\mathsf{A}\mathsf{B}$, where $\mathsf{A}$ is a…
In this paper two types of multgrid methods, i.e., the Rayleigh quotient iteration and the inverse iteration with fixed shift, are developed for solving the Maxwell eigenvalue problem with discontinuous relative magnetic permeability and…
A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating…
Under certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are…
In this paper, we present a new Hyperfast Second-Order Method with convergence rate $O(N^{-5})$ up to a logarithmic factor for the convex function with Lipshitz the third derivative. This method based on two ideas. The first comes from the…
We discuss an algorithm for the numerical evaluation of NLO multiparton processes. We focus hereby on the virtual part of the NLO calculation, i.e. on evaluating the one-loop integration numerically. We employ and extend the ideas of the…
The multivariate Ornstein-Uhlenbeck process is used in many branches of science and engineering to describe the regression of a system to its stationary mean. Here we present an $O(N)$ Bayesian method to estimate the drift and diffusion…
Inverse kinematics is an important and challenging problem in the operation of industrial manipulators. This study proposes a simple inverse kinematics calculation scheme for an industrial serial manipulator. The proposed technique can…