A novel sparse Gauss–Hermite quadrature filter is proposed using a sparse-grid method for multidimensional numerical integration in the Bayesian estimation framework. The conventional Gauss–Hermite quadrature filter is computationally expensive for multidimensional problems, because the number of Gauss–Hermite quadrature points increases exponentially with the dimension. The number of sparse-gr...

In many of the numerical methods for pricing American options based on the dynamic programming approach, the most computationally intensive part can be formulated as the summation of Gaussians. Though this operation usually requires O NN ′ work when there are N ′ summations to compute and the number of terms appearing in each summation is N , we can reduce the amount of work to O N +N ′ by usin...

We evaluate the eigenfields of an unstable Bessel-Gauss resonator (UBGR) by use of the transfer-matrix method in which the transverse profiles and their corresponding losses of the UBGR are considered as the eigenvectors and eigenvalues of a transfer matrix so that the dominant mode fields and their losses of the UBGR can be readily extracted in terms of the matrix eigenvalue algorithm. Moreove...

In this paper, we report that we have solved the shortest vector problem (SVP) over a 128-dimensional lattice, which is currently the highest dimension of the SVP that has ever been solved. The security of lattice-based cryptography is based on the hardness of solving the SVP in lattices. In 2010 Micciancio et al. proposed a Gauss Sieve algorithm for heuristically solving the SVP using list L o...

The paper presents a simple combinatorial method to encode 3-dimensional manifolds, basing on their Heegaard diagrams. The notion of a Gauss diagram of a 3-manifold is introduced. We check the conditions for a Gauss diagram to represent a closed manifold and a manifold with boundary.

In this study, paraphenylenediamine was first bonded to the fullerene and was optimized geometrically by Using the quantum chemistry methods. paraphenylenediamine was examined in the isolated state and in the fullerene-bonded state via carbon atoms. In the theoretical research, the simulation was done by the Gauss View software. Then, the bonding orbital calculation was done by using the NBO me...

We introduce a new family of symplectic integrators for canonical Hamiltonian systems. Each method in the family depends on a real parameter α. When α = 0 we obtain the classical Gauss collocation formula of order 2s, where s denotes the number of the internal stages. For any given non-null α, the corresponding method remains symplectic and has order 2s−2; hence it may be interpreted as an O(h2...

2 Numerical and Symbolic Integration 2 2.1 Cubature Formulae Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Constructing Cubature Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2.1 Interpolatory Cubature Formulae . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2.2 Ideal Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

This paper investigates the properties of smoothers in the context of algebraic multigrid (AMG) running on parallel computers with potentially millions of processors. The development of multigrid smoothers in this case is challenging, because some of the best relaxation schemes, such as the Gauss-Seidel (GS) algorithm, are inherently sequential. Based on the sharp two-grid multigrid theory from...

Aiming at a fast and robust simulation of large multibody systems with contacts and friction, this work presents a novel method for solving large cone complementarity problems by means of a fixed-point iteration. The method is an extension of the Gauss-Seidel and Gauss-Jacobi method with overrelaxation for symmetric convex linear complementarity problems. The method is proved to be convergent u...