Recent work by Nesterov and Stich (2016) showed that momentum can be used to accelerate the rate of convergence for block GaussSeidel in the setting where a fixed partitioning of the coordinates is chosen ahead of time. We show that this setting is too restrictive, constructing instances where breaking locality by running non-accelerated Gauss-Seidel with randomly sampled coordinates substantia...

A Seidel-type interface condition is considered for non-overlapping domain decomposition iterative methods. With a suitable pseudo-energy defined on interfaces, the convergence speed of the iterative scheme is shown to be as twice fast as that of the Jacobi scheme. Our analysis is entirely independent of the governing model problems of a specific type of partial differential equations, but depe...

A curious phenomenon when it comes to solving the linear system formulation of the PageRank problem is that while the convergence rate of Gauss–Seidel shows an improvement over Jacobi by a factor of approximately two, successive overrelaxation (SOR) does not seem to offer a meaningful improvement over Gauss–Seidel. This has been observed experimentally and noted in the literature, but to the be...

Some variants of the (block) Gauss–Seidel iteration for solution linear systems with M-matrices in Hessenberg form are discussed. Comparison results asymptotic convergence rate some regular splittings derived: particular, we prove that a lower-Hessenberg M-matrix $$\rho (P_{GS})\ge \rho (P_S)\ge (P_{AGS})$$ , where $$P_{GS}, P_S, P_{AGS}$$ matrices Gauss–Seidel, staircase, and anti-Gauss–Seidel...

Solving a set of simultaneous linear equations is probably the most important topic in numerical methods. For solving linear equations, iterative methods are preferred over the direct methods specially when the coefficient matrix is sparse. The rate of convergence of iteration method is increased by using Successive Relaxation (SR) technique. But SR technique is very much sensitive to relaxatio...

In this paper we construct an infinite family of Goethals-Seidel arrays and prove the theorem: If q = 4n − 1 is a prime power ≡ 3(mod 8), then there exists an Hadamard matrix of order 4n of Goethals-Seidel type.

Laurence Seidel, Adelin Albert, Jean-Olivier Defraigne, Nicos Labropoulos and Natzi Alain Nchimi, Jean-Paul Cheramy-Bien, T. Christian Gasser, Gauthier Namur, Pierre Gomez, Tomography Signaling and Biomechanical Properties in Unruptured Aortic Aneurysms F-Fluoro-Deoxy-Glucose Positron Emission 18 Multifactorial Relationship Between Print ISSN: 1941-9651. Online ISSN: 1942-0080 Copyright © 2013 ...