An Algebraic Characterization of B-convergent Runge-Kutta Methods.
An algebraic construction of discrete wavelet transforms
Discrete wavelets are viewed as linear algebraic transforms given by banded orthogonal matrices which can be built up from small matrix blocks satisfying certain conditions. A generalization of the finite support Daubechies wavelets is discussed and some special cases promising more rapid signal reduction are derived.
An algebraic theory of order
In this paper, we present an abstract framework which describes algebraically the derivation of order conditions independently of the nature of differential equations considered or the type of integrators used to solve them. Our structure includes a Hopf algebra of functions, whose properties are used to answer several questions of prime interest in numerical analysis. In particular, we show that, under some mild assumptions, there exist integrators of arbitrarily high orders for arbitrary (modified)...
An algorithm based on rolling to generate smooth interpolating curves on ellipsoids
We present an algorithm to generate a smooth curve interpolating a set of data on an -dimensional ellipsoid, which is given in closed form. This is inspired by an algorithm based on a rolling and wrapping technique, described in [11] for data on a general manifold embedded in Euclidean space. Since the ellipsoid can be embedded in an Euclidean space, this algorithm can be implemented, at least theoretically. However, one of the basic steps of that algorithm consists in rolling the ellipsoid, over...
An Algorithm for a Special Case of a Generalization of the Richardson Extrapolation Process.
An Algorithm for Best Approximate Solutions of Ax = b with a Smooth Strictly Convex Norm.
An algorithm for biparabolic spline
The paper deals with the computation of suitably chosen parameters of a biparabolic spline (ot the tensor product type) on a rectangular domain. Some possibilities of choosing such local parameters (concentrated, dispersed parameters) are discussed. The algorithms for computation of dispersed parameters (using the first derivative representation) and concentraced parameters (using the second derivative representation) are given. Both these algorithms repeatedly use the one-dimensional algorithms....
An Algorithm for Calculating One Subgradient of a Convex Function of Two Variables.
An algorithm for checking Hurwitz stability of K-symmetrizable interval matrices
An algorithm for determining if the inverse of a strictly diagonally dominant Stieltjes matrix is strictly ultrametric.
An Algorithm for Determining Redundant Inequalities and All Solutions to Convex Polyhedra.
An algorithm for determining the number of linearly independent comitants of a system of differential equations
An Algorithm for Discrete Linear Lp Approximation.
An algorithm for evolutionary surfaces.
An Algorithm for Gaussian Quadrature given Modified Moments.
An Algorithm for Generating Random Numbers With Binomial Distribution
An algorithm for Hermite-Birkhoff interpolation
An algorithm for model reduction in large electric power systems.
An algorithm for QMC integration using low-discrepancy lattice sets
Many low-discrepancy sets are suitable for quasi-Monte Carlo integration. Skriganov showed that the intersections of suitable lattices with the unit cube have low discrepancy. We introduce an algorithm based on linear programming which scales any given lattice appropriately and computes its intersection with the unit cube. We compare the quality of numerical integration using these low-discrepancy lattice sets with approximations using other known (quasi-)Monte Carlo methods. The comparison is based...
An Algorithm for Rational Interpolation Similar to the qd-Algorithm.