Showing papers in "Applied Numerical Mathematics in 1999"

TL;DR: A number of recently proposed preconditioning techniques based on sparse approximate inverses are considered, and an experimental comparison performed on one processor of a Cray C98 vector computer using sparse matrices from a variety of applications is presented.

TL;DR: It is proved that any classical Runge-Kutta method can be turned into an invariant method of the same order on a general homogeneous manifold, and a family of algorithms that are relatively simple to implement are presented.

TL;DR: New methods for solving nonsymmetric linear systems of equations with multiple right-hand sides based on global oblique and orthogonal projections of the initial matrix residual onto a matrix Krylov subspace are presented.

TL;DR: In this article, the general equations for the parametric sensitivity functions of a broad class of hybrid discrete/continuous dynamic systems where the continuous part is described by differential-algebraic equations (DAEs) are presented.

TL;DR: This paper compares different strategies for choosing a-priori an approximate sparsity structure of A −1 and exactly determines the submatrices that are used in the SPAI algorithm to compute one new column of the sparse approximate inverse M.

TL;DR: In this article, suboptimal boundary control strategies for the time-dependent, incompressible flow over the backward-facing step are considered and a frame for the derivation of the optimality systems for a general class of cost functionals is presented.

TL;DR: A wide variety of nonlinear convex optimization problems can be cast as problems involving linear matrix inequalities (LMIs), and hence efficiently solved using recently developed interior-point methods, including some interesting applications that are less well known and arise in statistics, optimal experiment design and VLSI.

TL;DR: The present combination of unstructured grids (enhanced geometrical flexibility) and good parallel performance (rapid turnaround) should make the present approach attractive to hydrodynamic design simulations.

TL;DR: In this article, a tensor-based approach for iterative numerical analysis of continuous time Markov chains (CTMCs) is introduced, which is a means to extend the size of analyzable state spaces significantly compared with conventional techniques.

TL;DR: In this paper, a theory of finite-type relations between polynomial sequences is developed, which contains semi-classical sequences and in particular the so-called coherent pairs.

TL;DR: In this paper, a new difference scheme on a special piecewise equidistant tensor-product mesh (a Shishkin mesh) for a model singularly perturbed convection-diffusion problem in two dimensions was proposed.

TL;DR: Three new Runge–Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODEs) with constant coefficients, which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient.

TL;DR: Fourier analysis is used to investigate the behaviour of the numerical error for a number of higher-order one-dimensional finite elements, and it is shown that the spurious modes have a contribution to the numericalerror that behaves in a reasonable manner, and that higher- order elements can be more accurate than lower-order elements.

TL;DR: A unified approach for the derivation and handling of N B-series methods, a general class of methods including all Runge-Kutta type methods, with special attention to the integration of Hamiltonian systems by symplectic methods.

TL;DR: This framework is an extension of the v-space approach that was developed by Kojima et al. (1991) for linear complementarity problems and allows us to interpret Nesterov-Todd type directions as Newton search directions to semidefinite programming.

TL;DR: In this paper, the authors consider a semidefinite programming (SDP) problem in which the objective function depends linearly on a scalar parameter and study the properties of the optimal objective function value as a function of that parameter.

TL;DR: This paper investigates ways to derive semidefinite programs from discrete optimization problems and deals with the approximation of integer problems both in a theoretical setting, and from a computational point of view.

TL;DR: An iterative Jacobi type method is formulated and its convergence has been proved, under certain conditions on the interval matrix, to solve systems of linear equations involving an interval square matrix and an interval right-hand side vector using interval arithmetic.

TL;DR: In this paper, it was shown that the instability arises from the use of explicit finite difference schemes rather than any failure of energy conservation, and this conjecture was further supported by an analysis of two further schemes.

TL;DR: This work proves the convergence of the LTSN method for the steady-state and time-dependent one-dimensional linear transport equation employing the C 0 semigroup theory and discrete schemes approach.

TL;DR: An extension of the Cayley–Hamilton identity is formulated, the controllability and observability matrices are derived, and Krylov's method is discussed in terms of such matrix response.

TL;DR: In this paper, the reservation price of an option in an economy with more than one risky security and where trade involves transaction costs is examined. And the authors suggest an approach to compute reservation prices using convex optimization.

TL;DR: The p-version finite element method for solving linear second order elliptic equations in an arbitrary sufficiently smooth domain is studied in the framework of the Domain Decomposition (DD) method and several DD preconditioners are obtained, which provide a low computational cost and a high degree of parallelization.

TL;DR: A method for solving parabolic partial differential equations (PDEs) using local refinement in time based on a domain decomposition finite element method that is a better fit than BDF methods in this context since local time stepping in different spatial regions precludes history information.

TL;DR: The evolution of plane curves obeying the equationvD.k/w herev is normal velocity andk curvature of the curve is studied in this article, where a numerical scheme for solving the governing equation and present numerical experiments are introduced and analyzed.

TL;DR: In this article, a robust spline approximation method for mth order boundary value problems described by nonlinear ordinary differential and integro-differential equations with m linear boundary conditions was proposed.

TL;DR: In this article, an inner preconditioned GMRES iteration to fixed tolerance and incomplete factorization (RILU, restricted to the diagonal) are considered, and numerical experiments for a fundamental test problem are included, with particular focus on communication costs associated with orthogonalization processes.

TL;DR: In this paper, the authors present a complexity analysis of the column generation method in the general semi-infinite case, in terms of the problem dimension, the radius of the largest Euclidean ball contained in the feasible set and the desired accuracy of the approximate solution.

TL;DR: In this article, the authors propose a different strategy, where the number of iterations is fixed, but the step size is controlled with respect to stability, and numerical tests show the effectiveness of this approach in comparison with an implicit scheme that iterates to a certain tolerance.

TL;DR: In this paper, the mixed finite element method over quadrilaterals was used as a solver to the non-Darcy flow equation, and a conservative Godunov-type scheme for the mass balance equations.