Showing papers in "Journal of Computational and Applied Mathematics in 1993"

TL;DR: In this article, the fundamental aspects of variational inequalities with major emphasis on the theory of existence, uniqueness, computational properties, various generalizations, sensitivity analysis and their applications are discussed.

TL;DR: A bibliography of references to cubature rules which have appeared since the publication of Stroud's book (1971) is presented in this paper, where the standard regions that are treated in this paper are the n-cube, the nsimplex, n-sphere and the entire space.

TL;DR: It is proved that as soon as eigen values of the original operator are sufficiently well approximated by Ritz values, GMRES from then on converges at least as fast as for a related system in which these eigenvalues (and their eigenvector components) are missing.

TL;DR: It is shown that the well-known Levinson algorithm for computing the inverse Cholesky factorization of positive definite Toeplitz matrices can be viewed as a special case of a more general process.

TL;DR: In this paper, the principal characterizations of the classical orthogonal polynomials with the method of the dual sequence are surveyed and two new characterizations are given, connected problems are discussed.

TL;DR: In this article, a categorized bibliography on roots of polynomials is presented, covering the period from the earliest times until late 1990, and the actual bibliography is on a diskette accompanying this issue, together with programs designed to print parts of the main work, such as entries belonging to a certain category.

TL;DR: In this paper, the authors present an introductory survey of orthogonal polynomials on Sobolev spaces and their applications in the analysis of spectral methods for partial differential equations.

TL;DR: It is demonstrated that the Nedelec method can be superconvergent at certain special points and the method is related to Yee's finite-difference scheme.

TL;DR: In this article, the connection with polynomials orthogonal with respect to |H| |ρ|, where ρ has an odd number of zeros in each interval[a2j, a2j+1], j = 1,…,l − 1, is shown.

TL;DR: Gosper's and Zeilberger's algorithms for summation of terminating hypergeometric series as well as the q-versions of these algorithms are described in a very rigorous way in this article.

TL;DR: In this paper, a generalization of first-and second-and third-and fourth-kind polynomials is presented, and a set of logarithmically singular integral transforms for which weighted first-, second-, third-, fourth-and fifth-and sixth-and seventh-and eight-and nine-and ten-and eleven-and twelve-and fourteen-and sixteen-and seventeen-and twenty-and nineteen-and thirty-first-and eighteen-and forty-and fifty-and sixty-eight-and eighty-and seventy-eight

TL;DR: In this article, a new theorem for the Newton method convergence is obtained, which is different from that of the Kantorovich theorem and therefore has theoretical and practical value, and it has been shown to be correct.

TL;DR: In this article, general algorithms based on transforming the problem into a system of m second-order problems, and on solving the problem as a (2m)th-order problem are proposed for obtaining the solution of the special nonlinear boundary-value problem.

TL;DR: In this paper, a class of remarkable series for 1/π of the form −C 3 π = ∑ n=0 ∞ A+nB C 3n (6n) (3n)(n) 3 where A, B, C are certain algebraic numbers were examined by Ramanujan.

TL;DR: Remez-type inequalities as discussed by the authors give a sharp uniform bound on [−1, 1] for real algebraic polynomials p of degree at most n if the Lebesgue measure of the subset of [− 1, 1], where |;p|; is at most 1, is known.

TL;DR: It is shown that methods based on a low-order predictor and a Runge-Kutta corrector are not efficient and that if predictor-corrector methods are to be used efficiently for solving nonstiff problems in parallel, then high-order predictors are required.

TL;DR: In this paper, the authors developed methods for numerically integrating the Schwarzian differential equation with a related linear differential equation, which can be used to map highly elongated regions such as channels for internal flow problems.

TL;DR: In this article, it was shown that if n 0 denotes the number of critical points eiwj, then for every n ⩾ n0 and N ⊆ 1, the zeros z(j, n, N) of ϱn(ψN; z) can be arranged so that limN → ∞z(j and n, n) = eiwJ for each of the frequencies wj. This result confirms one of the main parts of the conjecture given by Jones, Njastad and Saff (this journal (

TL;DR: A special modification of the criterion for the time required to achieve a preset probable error is introduced and a special approach to constructing Monte Carlo vector algorithms to be efficiently run on pipeline computers is considered.

TL;DR: Barlow and Spizzichino as mentioned in this paper analyzed general properties of Schur-concave survival functions and gave representation theorems, which are a finite population version of time-transformed exponential distributions.

TL;DR: In this paper, the generalized Jacobi polynomials and generalized Laguerre polynoms were studied for differential equations of the form Σ∞i=0ci(x)y(i)(x) = 0.

TL;DR: Numerical conformal mapping methods for regions with a periodic boundary have been developed that can deal with boundary curves of arbitrary forms and high-order quadrature rules have been implemented in order to increase accuracy of the mapping.

TL;DR: In this paper, a q-Jacobi polynomial generalization of the Legendre polynomials is presented, which makes use of the little q-jacobians.

TL;DR: An overview of matrix decomposition algorithms and how they can be expressed in terms of a unifying framework is provided and particular emphasis is placed on algorithms formulated recently by the authors for solving the linear systems arising in orthogonal spline collocation, that is, splineCollocation at Gauss points.

TL;DR: In this article, the density of polynomials in Sobolev-type function spaces defined on the compact interval [−1, 1] of the real line R was discussed.

TL;DR: In this paper, a program built in Mathematica symbolic language is introduced to construct the unique differential equation satisfied by the associated of any order of the classical class of polynomials.

TL;DR: In this paper, the problem of finding a Caratheodory function with the interpolation property F ( α n ) = w n for all n is formulated as follows, where n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

TL;DR: In this article, the Hellmann-Feynman theorem has been used to give the derivative of an eigenvalue with respect to a parameter, which can be applied in either a differential equations or a recurrence relations setting.

TL;DR: In this article, the convergence factors and stability regions of the iterated Runge-Kutta-Nystrom (RKN) correctors are investigated. But the authors focus on the indirect collocation RKN correctors.

TL;DR: In this article, a random walk polynomial sequence can be defined (and will be defined in this paper) as an orthogonal sequence of random walk measures with respect to a measure on [-1, 1] and the parameters (alfa)n in the recurrence relations Pn=1(x)=(x(alfa n)Pn(x)-snPn- 1(x) are nonnegative.