Showing papers in "Journal of Computational and Applied Mathematics in 1987"

TL;DR: A new graphical display is proposed for partitioning techniques, where each cluster is represented by a so-called silhouette, which is based on the comparison of its tightness and separation, and provides an evaluation of clustering validity.

TL;DR: In this article, the authors presented a new two-step 6th-order method with phase-lag (1/3 628 800) H8 for numerical integration of periodic initial value problems.

TL;DR: It will be shown how intermediate information obtained by the conjugate gradients (cg) algorithm can be used to solve f(A)x = b iteratively in an efficient way, for suitable functions f.

TL;DR: In this paper, a vector QD-algorithm which links two diagonals (P"r^s)"r and (P''r''s^+^1)"r was proposed.

TL;DR: Traduction anglaise d'un article en japonais publie en Aout 1970 dans la serie Kokyuroku Vol-91 (pp 82-118) as discussed by the authors.

TL;DR: In this article, an iterative method to solve the convex feasibility problem for a finite family of convex sets is presented, which consists in the application of a generalization of an acceleration procedure introduced by De Pierro, in a parallel version of the Subgradient Projections Method proposed by Censor and Lent.

TL;DR: In this paper, a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements was proposed. But the recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L 2 -norm than the piecewise constant gradient of the Ritz-Galerkin solution.

TL;DR: In this paper, the authors proposed a scheme for the automatic selection of the initial step size for ODE solvers, which can lead to more robust and efficient integration than its provision by a user, and is always more convenient.

TL;DR: In this article, the authors proposed a new numerical method for calculating state probabilities for queueing systems with more than one waiting line in parallel, based on power series expansions of state probabilities as functions of the traffic intensity of a system.

TL;DR: In this paper, the authors study two algorithms for the reconstruction of the exponents and coefficients of the Hankel matrix, and show that the error in the reconstructed exponents is of the order of the gap σn + 1/(σn − σ n + 1) between the smallest accepted singular value and the largest rejected singular value of a Hankel matrices constructed from the data.

TL;DR: In this article, the convergence of the sequence of diagonal Pade approximations towards f is established under the condition that there exists a weight @w, positive almost everywhere on the Toeplitz matrix of symbol g(cos @F).

TL;DR: In this article, the existence of singular nonlinear two-point boundary value problems is examined. But the authors focus on the class of nonlinear singular non-linear boundary value problem, and do not consider the singular case.

TL;DR: An improved algorithm PSVD for computing the singular subspace of a matrix corresponding to its smallest singular values is presented and can be three times faster than the classical SVD algorithm while the same accuracy can be maintained.

TL;DR: Combining the automatic quadratures method obtained and Sidi's extrapolation method makes an effective quadrature scheme for oscillatory infinite integral ∫ ∞ a ƒ( x ) cos ω x d x for which numerical examples are also presented.

TL;DR: In this paper, the existence of an optimal local spline interpolant for all orders is proved by increasing, in a specified manner, the set of partition points of the spline space.

TL;DR: In this article, the existence and uniqueness of solutions of the volume and smoothness problems that are used in variational grid generation are studied, and an analysis of the Euler-Lagrange (EL) equations near the identity is presented.

TL;DR: In this paper, a classification of linear (stationary) iterative methods for linear systems of algebraic equations is presented, with a focus on extrapolation, relaxation and relaxation.

TL;DR: In this article, an adaptive subroutine that computes an approximation to the integral of a function f ( x, y ) over a two dimensional region made up of triangles is presented.

TL;DR: In this paper, a simple product integration scheme is proposed to solve a nonlinear Volterra integro-differential equation with a weakly singular kernel and a non-smooth solution.

TL;DR: In this paper, it is shown that divergent oscillatory infinite integrals exist in the sense of Abel summability and that the W-transformation can be applied to them without any modifications.

TL;DR: In this article, the authors presented a new fourth-order finite difference method based on uniform mesh for the singular two-point boundary value problem, which provides O(h4)-convergent approximations for all α ∈ (0, 1), for α = 0 it reduces to the well-known fourth order method of Numerov for y = ƒ(x, y).

TL;DR: In this article, the convergence of sequences of integration rules applied to an improperly integrable function with an interior singularity is investigated, including the Gauss-Jacobi rules and the interpolatory integration rules based on the zeros of (1 − x 2 ) m P n−2m (α,β) (x), m0, 1 for certain values of α and β.

TL;DR: In this paper, the convergence of Lagrange interpolation at the zeros of orthogonal polynomials associated with Freud weights on R was investigated, and the results were sharp in L,, 1 < p G 2.

TL;DR: In this paper, the problem of finding an approximation to the conformal map of a simply-connected domain onto a rectangle R, where four specified points on ∂Ω are mapped respectively onto the four vertices of R, is studied.

TL;DR: In this paper, the stability analysis of one-step methods for the numerical solution of initial value problems is considered. But the focus is on stability of the methods with respect to the maximum norm.

TL;DR: In this paper, a multistep rational approximation of a bounded, strongly continuous semigroup on a Banach space is considered and the convergence of the time step to zero under a weak form of A-stability assumption is studied.

TL;DR: In this paper, the authors derived feasible structures for integration formulas on the surface of the s-dimensional sphere, for s = 3 and s = 4 for formulas of degrees 3 to 17, and for general s of degree 3 to 9.

TL;DR: In this paper, the authors investigate the asymptotic behavior of Hermite-Pade polynomials of Latin type, which are formed from differential or algebraic expressions involving a meromorphic function.

TL;DR: In this paper, asymptotic expansions in the analysis of the @D^2 and @q"2-algorithms leads to modified iterated versions of the first one and to combinations with the iterated @q'' 2-algorithm.