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Showing papers in "Journal of Computational and Applied Mathematics in 1996"


Journal ArticleDOI
TL;DR: In this paper, the authors considered the smoothing of the approximating functions at concave boundaries and the speedup of the calculation of the approximate functions and their derivatives and showed a moderate improvement in the accuracy of the smoothed interpolant.

261 citations


Journal ArticleDOI
Michael S. Floater1, Armin Iske1
TL;DR: A hierarchical scheme is presented for smoothly interpolating scattered data with radial basis functions of compact support using successive Delaunay triangulations, which is rotationally invariant and has good reproduction properties.

254 citations


Journal ArticleDOI
David Levin1
TL;DR: In this paper, a collocation method for approximating integrals of rapidly oscillatory functions is presented, which is efficient for integrals involving Bessel functions Jv(rx) with large oscillation parameter r.

233 citations


Journal ArticleDOI
TL;DR: A new preconditioning technique for the restarted GMRES algorithm is presented, based on an invariant subspace approximation which is updated at each cycle, which gives a more robust scheme at a low cost of operations and memory.

219 citations


Journal ArticleDOI
TL;DR: A practical numerical algorithm for bounding the bilinear form, where the matrix A is only referenced through matrix-vector multiplications is studied and a Monte Carlo method is presented to efficiently estimate the trace of the inverse and the determinant of a large sparse matrix.

217 citations


Journal ArticleDOI
TL;DR: Fully symmetric interpolatory integration rules are constructed for multidimensional integrals over infinite integration regions with a Gaussian weight function in this paper, where the points for these rules are determined by successive extensions of the one-dimensional three-point Gauss-Hermite rule.

214 citations


Journal ArticleDOI
TL;DR: In this paper, a method for solving general inverse LP problems including upper and lower bound constraints is suggested, based on the optimality conditions for LP problems, and when applied to inverse minimum cost flow problem or inverse assignment problem, they are able to obtain strongly polynomial algorithms.

142 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed subgrid scale models for nonsymmetric, linear evolution operators by applying the variational multiscale method in space-time, which is a paradigm for bubble function finite element methods and provides a theoretical and practical framework for the development of so-called stabilized methods.

137 citations


Journal ArticleDOI
TL;DR: Experimental results indicate that, especially for methods with short recurrences like BiCGSTAB, it is advantageous to preserve the orthogonality in the inner method, and it is shown that in terms of matrix-vector products, this modification (almost) always leads to better convergence.

131 citations


Journal ArticleDOI
TL;DR: In this paper, the authors propose a space of polynomial splines defined on planar traingulations for fitting scattered data in the plane, using macro-element and minimal energy splines.

131 citations


Journal ArticleDOI
TL;DR: Orthogonal matrix polynomials, both on the real line and on the unit circle, have properties which are natural generalizations of properties of scalar orthogonality, appropriately modified for the matrix calculus as mentioned in this paper.

Journal ArticleDOI
TL;DR: In this paper, thirtyeight summation closely related to Whipple's theorem in the theory of the generalized hypergeometric series are obtained, and some limiting cases are also considered.

Journal ArticleDOI
TL;DR: In this article, the problem of finding all polynomial sequences which are at the same time Appell polynomials and d-orthogonal is solved, and a sequence of these polynomorphisms is obtained, where all the elements of its (d + 1)-order recurrence are explicitly determined.

Journal ArticleDOI
TL;DR: In this paper, the linearized form of an evolution equation used to model viscoelasticity and heat conduction in materials with memory is discretized in time using several schemes based on the backward Euler and Crank-Nicolson methods.

Journal ArticleDOI
TL;DR: Some new developments of the numerical methods, for example, 2-cycle SOR method and preconditioned conjugate gradient method, for generalized least squares problems are presented.

Journal ArticleDOI
TL;DR: Askey and Wilson as discussed by the authors showed that the Askey-wilson polynomials satisfy a q-difference equation of the form a(k)(p(n)(s(qk))) - p(n)p(s(k)) + b(k)(p n)(s)k/q)) -p n(n), p n(m)m, p n)(m, m, s(k)), n = 0, 1.

Journal ArticleDOI
TL;DR: In this article, implicit difference schemes of O(k 4 + k 2 h 2 + h 4 ) were developed for the efficient numerical integration of the system of one space second order nonlinear hyperbolic equations with variable coefficients subject to appropriate initial and Dirichlet boundary conditions.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a new set of partial differential equations (PDEs) which can be seen as a generalization of the classical eikonal and transport equations, to allow for solutions with multiple phases.

Journal ArticleDOI
TL;DR: In this article, a nonsymmetric version of the Poisson kernel with Askey-Wilson polynomials is considered and the theory of q-Fourier transformation is further extended.

Journal ArticleDOI
TL;DR: In this paper, the authors developed and analyzed least-squares approximations for Stokes and elasticity problems, which do not require that the classical Ladyzhenskaya-Babǔska-Brezzi (LBB) condition be satisfied.

Journal ArticleDOI
TL;DR: In this article, the question of convergence of boundary value methods (BVMs) along with the linear stability theory is discussed, along with some numerical examples on stiff test problems are also presented.

Journal ArticleDOI
TL;DR: In this paper, a compact approximate method in limiting form for calculating the solution of Burgers' equation with appropriate boundary conditions is presented, and the results obtained by present method are found to be in good agreement with those due to earlier authors.

Journal ArticleDOI
TL;DR: In this article, a set of orthogonal polynomials with eight independent q s is defined, which generalizes the Laguerre polynomial, and the moments of the measure for these polynoms are the generating functions for permutations according to eight different statistics.

Journal ArticleDOI
TL;DR: A planar cubic Bezier curve segment that is a spiral, i.e., its curvature varies monotonically with arc-length, is discussed and is suitable for general curve design applications in which fair curves are important.

Journal ArticleDOI
TL;DR: In this paper, basic equations and conditions of theory of micropolar bodies with voids are presented, and the initial-boundary value problem, in this context, is formulated.

Journal ArticleDOI
TL;DR: A variant of the preconditioned conjugate gradient method to solve generalized least squares problems is presented and Freund's comparison result for regular least square problems is extended to generalized most squares problems.

Journal ArticleDOI
TL;DR: In this article, a family of predictor-corrector exponential Numerov-type methods is developed for numerical integration of the one-dimensional Schrodinger equation, which can be fitted automatically to exponential functions.

Journal ArticleDOI
TL;DR: In this paper, the asymptotic behavior of the function Γ(α,x;b) = ∫ x ∞ t α−1 e −t− b t dt, x > 0, α> 0, b ⩾ 0, as x tends to infinity.

Journal Article
TL;DR: This test set is maintained by the project group for Parallel IVP Solvers of CWI, department of Numerical Mathematics and the group invites everyone to contribute new test problems to this test set.

Journal ArticleDOI
TL;DR: In this paper, a general theory for writing multi-variate Fourier transforms or convolutions of radial functions as simple univariate operations is provided, and an interesting group of operators (Iα)xϵR with Iα−α = Iα Iβ = Iβ Iα is defined.