Showing papers in "Journal of Computational and Applied Mathematics in 2000"

TL;DR: The Kronecker product has a rich and very pleasing algebra that supports a wide range of fast, elegant, and practical algorithms and several trends in scientific computing suggest that this important matrix operation will have an increasingly greater role in the future.

TL;DR: Direct search methods are characterized by the absence of the construction of a model of the objective function as discussed by the authors, which is a characteristic of direct search methods for unconstrained optimization, and a modern perspective on this classical family of derivative-free algorithms is given in this paper.

TL;DR: In this article, a variety of fractional evolution processes are reviewed, whose solutions turn out to be related to Mittag-Leffler-type functions, and the chosen equations are the simplest of the fractional calculus and include the Abel integral equations of the second kind.

TL;DR: This work reviews some of the key developments in the modern era of interior-point methods, including comments on both the complexity theory and practical algorithms for linear programming, semi-definite programming, monotone linear complementarity, and convex programming over sets that can be characterized by self-concordant barrier functions.

TL;DR: An overview on applications of interval arithmetic is given and verification methods for linear systems of equations, nonlinear systems, the algebraic eigenvalue problem, initial value problems for ODEs and boundary valueblems for elliptic PDEs of second order are discussed.

TL;DR: In this article, the main research developments in the area of iterative methods for solving linear systems during the 20th century are described and compared, and the most signicant contributions during the past century are compared to one another.

TL;DR: In this paper, the authors review iterative methods for the determination of a suitable value of the regularization parameter by the L-curve criterion and the solution of regularized systems of algebraic equations.

TL;DR: The use of Krylov-subspace methods for generating reduced-order models of linear subcircuit models that preserve the passivity of linear RLC subcircuits are described.

TL;DR: In this article, the existence of infinitely many local minima of the functional Φ+λΨ for each sufficiently large λ∈ R was studied for a reflexive real Banach space and two weakly lower semicontinuous functionals.

TL;DR: The intention of this contribution is to sketch the main developments of this century, especially as they relate to one another, and to give an impression of the state of the art at the turn of the authors' century.

TL;DR: In this paper, the authors analyze both the qualitative and quantitative role that delays play in basic time-lag models proposed in population dynamics, epidemiology, physiology, immunology, neural networks and cell kinetics.

TL;DR: Truncated-Newton methods are a family of methods for solving large optimization problems that have been a collection of powerful, flexible, and adaptable tools for large-scale nonlinear optimization.

TL;DR: In this article, two discretization methods are discussed that transcribe optimal control problems into nonlinear programming problems for which SQP-methods provide efficient solution methods, which can be used also for a check of second-order sufficient conditions and for a post-optimal calculation of adjoint variables.

TL;DR: In this article, the scale-invariant solutions of the mixed problem of signalling type for the time-fractional diffusion-wave equation are given in terms of the Wright function in the case 0 <α< 1 and in terms with the generalized Wright function for the case 1 <α < 2.

TL;DR: Certain models of asynchronous iterations, using a common theoretical framework, are reviewed, including nonsingular linear systems, nonlinear systems, and initial value problems that arise naturally on parallel computers.

TL;DR: This work provides an introduction to the general method of sequential quadratic programming and shows its relationship to recent developments in interior-point approaches, emphasizing large-scale aspects.

TL;DR: In this paper, the basic notions of automatic differentiation and their extensions are introduced and described in the context of nonlinear optimization and some illustrative examples are given. But they do not consider the automatic differentiation problem in the nonlinear setting.

TL;DR: Various forms of complementarity problems are described along with a few sample applications, which provide a sense of what types of problems can be addressed effectively with complementarity Problems.

TL;DR: Some recent results and current research trends on deterministic and stochastic global optimization and global continuous approaches to discrete optimization are highlighted.

TL;DR: Practical quasi-Newton methods for solving nonlinear systems are surveyed in this paper, with a particular emphasis on the methods that satisfy the secant equation at every iteration, which are called here, as usually, secant methods.

TL;DR: This survey paper follows the main strands in the developments of these methods, both for general problems, stiff systems, and for many of the special problem types that have been gaining in significance as the century draws to an end.

TL;DR: The design of optimal experiments for chemical processes described by nonlinear DAE models are designed and solved using a structured SQP method and the performance of this approach is demonstrated for an application to chemical reaction kinetics.

TL;DR: In this article, the Mittag{Leer (M{L) functions have been compared with generalized operators of integration and dierention of the so-called Gelfond{Leontiev-type and Borel{Laplace-type integral transforms.

TL;DR: A survey of the results in connection with the minimal state-space realization problem for linear time-invariant systems can be found in this paper, where some extensions of this problem to other classes of systems and point out some related problems.

TL;DR: In this paper, a short survey of multivariate polynomial interpolation is presented, including a pioneering paper by Kronecker in the 19th century, which has received and continues receiving not deep but constant attention.

TL;DR: The authors provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new.

TL;DR: In this paper, the authors considered the problem of numerical solution of stochastic delay differential equations of Ito form d X(t)=f(X(t),X (t−τ)) d t+g(X,t,X(τ)), d W(t,T), t∈[0,T] with given f,g, Wiener noise W and given τ>0, with a prescribed initial function Ψ.

TL;DR: The collocation methods introduced in this paper are based on linear combinations of trigonometric functions and powers and provide better approximations for oscillatory solutions of initial-value problems for differential equations of the special form y″=f(x,y).

TL;DR: In this paper, both the point and block SOR methods are considered for the solution of a linear system of the form Ax=b, where A∈ C n,n and b∈ c n ⧹{0}.