DeepAI AI Chat
Log In Sign Up

Accelerating the Distributed Kaczmarz Algorithm by Strong Over-relaxation

by   Riley Borgard, et al.

The distributed Kaczmarz algorithm is an adaptation of the standard Kaczmarz algorithm to the situation in which data is distributed throughout a network represented by a tree. We isolate substructures of the network and study convergence of the distributed Kazmarz algorithm for relatively large relaxation parameters associated to these substructures. If the system is consistent, then the algorithm converges to the solution of minimal norm; however, if the system is inconsistent, then the algorithm converges to an approximated least-squares solution that is dependent on the parameters and the network topology. We show that the relaxation parameters may be larger than the standard upper-bound in literature in this context and provide numerical experiments to support our results.


A Kaczmarz Algorithm for Solving Tree Based Distributed Systems of Equations

The Kaczmarz algorithm is an iterative method for solving systems of lin...

The standard form and convergence theory of the relaxation Kaczmarz-Tanabe method for solving linear systems

The Kaczmarz method is a popular iterative method for solving consistent...

A doubly relaxed minimal-norm Gauss-Newton method for nonlinear least-squares

When a physical system is modeled by a nonlinear function, the unknown p...

Unexpected convergence of lattice Boltzmann schemes

In this work, we study numerically the convergence of the scalar D2Q9 la...

Convergence and Semi-convergence of a class of constrained block iterative methods

In this paper, we analyze the convergence projected non-stationary bloc...

Acceleration of Cooperative Least Mean Square via Chebyshev Periodical Successive Over-Relaxation

A distributed algorithm for least mean square (LMS) can be used in distr...

A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in Graph Data

In this work, we present the Bregman Alternating Projected Gradient (BAP...