Related papers: Hierarchically deflated conjugate gradient
The one-dimensional real line of coordinates is replaced, for simplification or approximation purposes, by an N-plet of the so called Gauss-Hermite grid points. These grid points are interpreted as the eigenvalues of a tridiagonal matrix…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
We propose a regularization of four dimensional chiral gauge theories using six-dimensional Dirac fermions. In our formulation, we consider two different mass terms having domain-wall profiles in the fifth and the sixth directions,…
In this paper, we investigate a five-dimensional Dirac fermion on a quantum graph that consists of a single vertex and $N$ loops. We find that the model possesses a rich structure of boundary conditions for wavefunctions on the quantum…
We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present the implementation of the RHMC algorithm for simulating dynamical Wilson fermions. A first dataset is presented…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
In this work we extend the shifted Laplacian approach to the elastic Helmholtz equation. The shifted Laplacian multigrid method is a common preconditioning approach for the discretized acoustic Helmholtz equation. In some cases, like…
The high computational cost involved in modeling of the progressive fracture simulations using large discrete lattice networks stems from the requirement to solve {\it a new large set of linear equations} every time a new lattice bond is…
The purpose of this paper is to introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M…
We propose Riemannian preconditioned algorithms for the tensor completion problem via tensor ring decomposition. A new Riemannian metric is developed on the product space of the mode-2 unfolding matrices of the core tensors in tensor ring…
We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme…
This paper investigates the efficient solution of penalized quadratic regressions in high-dimensional settings. A novel and efficient algorithm for ridge-penalized quadratic regression is proposed, leveraging the matrix structures of the…
In this paper, we study FPGA based pipelined and superscalar design of two variants of conjugate gradient methods for solving Laplacian equation on a discrete grid; the first version corresponds to the original conjugate gradient algorithm,…
We show that the number Z of q-edge-colourings of a simple regular graph of degree q is deducible from functions describing dimers on the same graph, viz. the dimer generating function or equivalently the set of connected dimer correlation…
We find the renormalisation coefficients of the quark field and the flavour non-singlet fermion bilinear operators for the domain wall fermion action, in the regularisation independent (RI) renormalisation scheme. Our results are from a…
The conjugate gradient (CG) method, a standard and vital way of minimizing the energy of a variational state, is applied to solve several problems in Skyrmion physics. The single-Skyrmion profile optimizing the energy of a two-dimensional…
The recent solution to the fermion sign problem allows, for the first time, the use of cluster algorithm techniques to compute certain fermionic path integrals. To illustrate the underlying ideas behind the progress, a cluster algorithm is…
Multigrid solvers are among the most efficient methods for solving the Poisson equation, which is ubiquitous in computational physics. For example, in the context of incompressible flows, it is typically the costliest operation. The present…
We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…
Complex-variable matrix optimization problems (CMOPs) in Frobenius norm emerge in many areas of applied mathematics and engineering applications. In this letter, we focus on solving CMOPs by iterative methods. For unconstrained CMOPs, we…