Showing papers in "Journal of Computational and Applied Mathematics in 1989"

TL;DR: In this article, the s -step Conjugate Gradient Method (S-CGM) was introduced for linear systems of equations and the convergence of the S-SGM was discussed.

TL;DR: The basic questions for a self-adaptive solution of nonlinear systems of elliptic and parabolic PDEs by a variable step size/variable order finite difference method on vector computers are discussed.

TL;DR: In particular, the backward Euler method turns out to be stable with respect to all the given definitions of numerical stability as discussed by the authors, which is reminiscent of that from the nonlinear, stiff ODE field.

TL;DR: In this paper, a numerical method for the computation of heteroclinic orbits connecting two saddle points in ℝ2 is presented, which can be computed to very high period due to an integral phase condition and an adaptive discretization.

TL;DR: In this article, it is shown that it is possible to find Cornu spirals with a micro-computer and that the radii of the circles used will limit and control the curvature of the whole design curve.

TL;DR: In this paper, a group theoretical approach for the detection of bifurcation points and the computation of (multiple) Hopf points is presented. But it is aimed to numerical applications.

TL;DR: In this article, a Steffensen-like iterative method is proposed which starts from a guessed sequence {un(0)} for the approximation of {yn} and allows certain computations to be performed in parallel.

TL;DR: The role of elimination trees in the exploitation of sparsity and the identification of parallelism is explained, and pseudo-code algorithms are provided for some of the important algorithms.

TL;DR: In this paper, the authors develop and analyze schemes for accelerating the convergence of the alternating projections method for finding the projection of a point onto the intersection of a finite number of subspaces of a Hilbert space.

TL;DR: Brown et al. as discussed by the authors revisited and implemented an algorithm for solving radial Schrodinger equations in a more accurate way, which was firstly applied to equations where potentials are present which are finite at the origin and which have an asymptotic behaviour V (r → 0 as r → ∞).

TL;DR: A limited processor version of the recursive doubling algorithm for the solution of tridiagonal linear systems using O( n / p + log p ) parallel arithmetic steps on a parallel computer with p n processors.

TL;DR: In this article, the authors considered the accuracy of the split-step solution for wave propagation in random media, both analytically and numerically, and showed that both step-wise and cumulative accuracy for the moments is greater than it is for the wavefield itself.

TL;DR: In this paper, the authors studied the convergence of dynamic iteration methods by applying them to linear DAE systems and showed that convergence rate can be studied by similar means as for ODE's and that it is critical for convergence to preserve the structure of DAE system when it is split for the iteration.

TL;DR: In this paper, a constructive proof for existence and unicity of the rational R,,, belonging to gM,v, M > 0, N > 0 having prescribed N poles and interpolating M + 1 Hermite data is given.

TL;DR: A survey of the available numerical methods for approximating the conformal map can be found in this article, where the authors also illustrate the practical significance of the map by presenting a number of applications involving the solution of Laplacian boundary value problems.

TL;DR: Two fundamental approaches for determining the eigenvalues and eigenvectors of dense symmetric matrices on machines such as the Alliant FX/8 and CRAY X-MP are discussed.

TL;DR: In this paper, the 4th-order differential equation satisfied by co-recursive polynomials of the classical orthogonal polynomorphisms is explicitly defined and conjectured for the LEGENDRE and BESSEL cases.

TL;DR: Runs are shown of the code multiprocessed under the SCHEDULE package from Argonne which presents a portable interface to users of parallel machines, allows the user to define the computational graph, and has very useful graphic output to a SUN workstation.

TL;DR: In this paper, the authors present and discuss the theory for a class of non-local boundary value problems for partial differential equations and point out its applications to numerical analysis, motivated by many important applications, especially by resistivity well-logging in petroleum exploitation.

TL;DR: In this paper, a wider class of matrices, called almost Stieltjes matrices (SSMs), is used as reference class for the conditioning analysis of finite element approximations of large multidimensional steady-state diffusion problems.

TL;DR: The reasons that estimates of the error over a given region of integration may fail in representing an upper bound for the actual error are discussed.

TL;DR: In this article, the authors present a new approach to the theoretical and computational analysis of the bifurcating branches at this singular point using a symmetry in the system used to calculate Hopf bifurbcations.

TL;DR: In this paper, a potential problem with a nonlinear boundary condition was studied and the solvability of the collocation method was analyzed using the theory of a-proper and a-stable mappings.

TL;DR: In this article, some new quasi-Monte Carlo methods for the solution of the Boltzmann equation in a simplified case are described, and the errors of the methods are estimated by means of the discrepancies of the sequences used for performing the Monte Carlo quadratures.

TL;DR: In this article, the Predictor-Corrector continuation method for large sparse linear systems is studied, and a numerical example involving bifurcating branches of a nonlinear eigenvalue problem is given.

TL;DR: By a limit analysis and accompanying numerical tests of elliptic difference equations with anisotropy it is found that methods based on line-block factorizations are to be preferred in general; among the vectorizable methods a line method where Euler expansion of the factors of the pivot blocks is used, is the most robust with respect to the problem parameters.

TL;DR: A survey of recent developments in the numerical treatment of such functional equations, with the focus being on equations with infinite delay, is given in this paper, where a number of numerical aspects that are not yet understood well.

TL;DR: In this paper, a theoretical foundation is given for a recently proposed continuation method for nonlinear variational inequalities that depend on a parameter and extensive numerical results are obtained that not only show the effectiveness of the proposed method, but also clarify the phenomenon of discrete or spurious transition points observed earlier.

TL;DR: In this article, a path-following multi-grid continuation strategy was developed combining a nested iteration type scheme as predictor with a subsequent multigrid method as corrector for parameter-dependent nonlinear elliptic obstacle problems.