We investigate the use of partial Gauss elimination as a preprocessing step to parity game solving. Gauss elimination is a well-known technique for solving Boolean equation systems. We present an Θ(V ) time algorithm for exhaustive partial Gauss elimination on parity games. Experimental validation shows that this approach is probably not feasible for speeding up the solving of real-world parity...

Gauss-Seidel method is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for po...

We present an algorithm for computing Gauss sums over Fq for large prime powers q. This allows us to find the exact values of Gauss sums in many previously intractable cases. The efficient computation of such Gauss sums up to multiplication with a root of unity is achieved by using Stickelberger’s factorization of Gauss sums, an application of the Fincke-Pohst algorithm, and fast arithmetic for...

Filon-Simpson quadrature rules are derived for integrals of the type ∫ b a dx f(x) sin(xy)/(xy) and ∫ b a dx f(x) 4 sin(xy/2)/(xy) which are needed in applications of the worldline variational approach to Quantum Field Theory. These new integration rules reduce to the standard Simpson rule for y = 0 and are exact for y → ∞ when a = 0 and f(0) 6= 0. The subleading term in the asymptotic expansio...

We give an estimate of the Gauss curvature for minimal surfaces in Rm whose Gauss map omits more than m(m + 1)/2 hyperplanes in P(C).

Introduction In this paper we present a modification of Gauss-Huard's method for solving dense linear systems that allows an efficient implementation on machines with a hierarchical memory structure. GaussHuard's method resembles Gauss-Jordan's method in the fact that it reduces the given system by elementary transformations to a diagonal system and it resembles regular Gaussian elimination in ...

Analytical expressions of the elements of a cross spectral density matrix are derived to describe the partially coherent Lorentz-Gauss beam propagating in uniaxial crystals orthogonal to the x-axis. The intensity and degree of polarization for the partially coherent Lorentz-Gauss beam propagating in uniaxial crystals orthogonal to the x-axis are also presented. The evolution properties of the p...

We study Gauss-Kronrod quadrature formulae for the Jacobi weight function «/"'"'(t) = (l-i)Q(l + t)'3 and its special case a = ß = X^ of the Gegenbauer weight function. We are interested in delineating regions in the (a, /3)-plane, resp. intervals in A, for which the quadrature rule has (a) the interlacing property, i.e., the Gauss nodes and the Kronrod nodes interlace; (b) all nodes contained ...

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...

This paper proposes a direct approach for solving optimal control problems. The time domain is divided into multiple subdomains, and a Lagrange interpolating polynomial using the Legendre–Gauss– Lobatto points is used to approximate the states and controls. The state equations are enforced at the Legendre–Gauss–Lobatto nodes in a nonlinear programming implementation by partial Gauss–Lobatto qua...