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In this paper a Galerkin method is used to construct series solutions of a homogeneous Sturm-Liouville problem defined on [0, &pie;]. The series constructed are shown to converge to a specified du Bois-Reymond function f in L² [0,&Pie;]. It is then shown that the series solutions can be made to converge uniformly to the specified du Bois-Reymond function when averaged by the Cesaro-one summability method. Therefore, in the Cesaro-one sense, every continuous function / o n [0, &Pie;] is the uniform limit of solutions of non-homogeneous Sturm-Liouville problems. [ABSTRACT FROM AUTHOR]

In this paper we propose a new criterion, minimum aberration majorization, for comparing non-isomorphic saturated designs. This criterion is based on the generalized word-length pattern proposed by Ma and Fang (Metrika 53 (2001) 85) and Xu and Wu (Ann. Statist. 29 (2001) 1066) and majorization theory. The criterion has been successfully applied to check non-isomorphism and rank order saturated designs. Examples are given through five non-isomorphic L16(215) designs and two L27(313) designs. [Copyright &y& Elsevier]

A mixed partition of PG(2n-1,q2) is a partition of the points of PG(2n-1,q2) into (n-1)-spaces and Baer subspaces of dimension 2n-1. In (Bruck and Bose, J. Algebra 1 (1964) 85) it is shown that such a mixed partition of PG(2n-1,q2) can be used to construct a (2n-1)-spread of PG(4n-1,q) and hence a translation plane of order q2n. In this paper, we provide several new examples of such mixed partitions in the case when n=2. [Copyright &y& Elsevier]

An effective method of chaotification via time-delay feedback for a simple finite-dimensional continuous-time autonomous system is made rigorous in this paper. Some mathematical conditions are derived under which a nonchaotic system can be controlled to become chaotic, where the chaos so generated is in a rigorous mathematical sense of Li–Yorke in terms of the Marotto theorem. Numerical simulations are given to verify the theoretical analysis. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, we study a 2D dissipative Klein–Gordon equation with periodic boundary condition. The existence and uniqueness of a time-periodic solution is proved by the Galerkin method and Leray–Schauder fixed point theorem. [Copyright &y& Elsevier]

The aim of this paper is to generalize the results of Yamada et al. [Yamada, I., Ogura, N., Yamashita, Y., Sakaniwa, K. (1998). Quadratic approximation of fixed points of nonexpansive mappings in Hilbert spaces. Numer. Funct. Anal. Optimiz. 19(l):165-190], and to provide complementary results to those of Deutsch and Yamada [Deutsch, F., Yamada, I. (1998). Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings. Numer. Funct. Anal. Optim. 19(1&2):33-56] in which they consider the minimization of some function d over a closed convex set F, the nonempty intersection of N fixed point sets. We start by considering a quadratic function θ and providing a relaxation of conditions of Theorem 1 of Yamada et al. (1998) to obtain a sequence of fixed points of certain contraction maps, converging to the unique minimizer of θ over F. We then extend Theorem 2 and obtain a complementary result to Theorem 3 of Yamada et al. (1998) by replacing the condition lim n → ∞ (λn - λn+1)/λ²n+1 = 0 on the parameters by the more general condition lim n → ∞ λn / λn+1 = 1. We next look at minimizing a more general function θ than a quadratic function which was proposed by Deutsch and Yamada (1998) and show that the sequence of fixed points of certain maps converge to the unique minimizer of 9 over F. Finally, we prove a complementary result to that of Deutsch and Yamada (1998) by using the alternate condition on the parameters. [ABSTRACT FROM AUTHOR]

In the paper, a new trust region algorithm is given for nonlinear inequality constrained optimization problems. Motivated by a dual problem introduced by Han and Mangasarian [Han, S. P., Mangasarian, O. L. (1983). A dual differentiable exact penalty function. Math. Programming 25:293-306], which is a nonnegatively constrained maximization problem, we construct a trust region algorithm for solving the dual problem. At each iteration, we only need to minimize a quadratic subproblem with simple bound constraints. Under the condition that the iterate sequence generated by the algorithm is contained in some bounded closed set, any accumulation point of the sequence is a Karush- Kuhn-Tucker point of the original problem. [ABSTRACT FROM AUTHOR]

In many wavelets applications, a scalar product of given function with the scaling function has to be calculated. For deriving effective one point quadrature formulas, the relation among the first scaling moment and the second one is crucial. In this paper, new relations among scaling moments are deduced. [ABSTRACT FROM AUTHOR]

In this paper, we consider a general primal-dual nonlinear rescaling (PDNR) method for convex optimization with inequality constraints. We prove the global convergence of the PDNR method and estimate the error bounds for the primal and dual sequences. In particular, we prove that, under the standard second-order optimality conditions, the error bounds for the primal and dual sequences converge to zero with linear rate. Moreover, for any given ratio 0 < γ < 1, there is a fixed scaling parameter kγ > 0 such that each PDNR step shrinks the primal-dual error bound by at least a factor 0 < γ < 1, for any k ≥ kγ. The PDNR solver was tested on a variety of NLP problems including the constrained optimization problems (COPS) set. The results obtained show that the PDNR solver is numerically stable and produces results with high accuracy. Moreover, for most of the problems solved, the number of Newton steps is practically independent of the problem size. [ABSTRACT FROM AUTHOR]

This paper describes and compares several effective methods for the numerical solution of one-dimensional Stefan problems. It is not intended to be an exhaustive review but is restricted to a range of problems and geometries including melting in the half-plane, outward cylindrical solidification and outward spherical solidification. From the limited comparison of numerical results obtained, some helpful comments can be made which may prove valuable in the future use of these methods. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we develop techniques for computing elementwise conservative approximations of the flux on element boundaries for the continuous Galerkin method. The technique is based on computing a correction of the average normal flux on an edge or face. The correction is a jump in a piecewise constant or linear function. We derive a basic algorithm which is based on solving a global system of equations and a parallel algorithm based on solving local problems on stars. The methods work on meshes with different element types and hanging nodes. We prove existence, uniqueness, and optimal order error estimates. Lastly, we illustrate our results by a few numerical examples. [ABSTRACT FROM AUTHOR]

We present an algorithm to compute the one-dimensional stable manifold of a saddle point for a planar map. In contrast to current standard techniques, here it is not necessary to know the inverse or approximate it, for example, by using Newton's method. Rather than using the inverse, the manifold is grown starting from the linear eigenspace near the saddle point by adding a point that maps back onto an earlier segment of the stable manifold. The performance of the algorithm is compared to other methods using an example in which the inverse map is known explicitly. The strength of our method is illustrated with examples of noninvertible maps, where the stable set may consist of many different pieces, and with a piecewise-smooth model of an interrupted cutting process. The algorithm has been implemented for use in the DsTool environment and is available for download with this paper. [ABSTRACT FROM AUTHOR]

Abstract: The scheduling problems studied in this paper concern the two-stage no-wait flowshops with parallel machines under the objective function of the minimization of the maximum completion time. A new heuristic algorithm, i.e., the minimum deviation algorithm, is developed to solve the problems. In order to evaluate the average case performance of the algorithm, we design numerical experiments to compare the effectiveness of the algorithm with that of the other approximation algorithms. Extensive simulations are conducted under different shop conditions, and the results statistically show that the minimum deviation algorithm performs well under most of the situations. [Copyright &y& Elsevier]

The goal of this paper is to present some numerical results for the one-dimensional denoising problem by using the nonlinear multiscale representations. We introduce modified thresholding strategies in this new context which give significant significant improvements for one-dimensional denoising problems. To cite this article: B. Matei, C. R. Acad. Sci. Paris, Ser. I 338 (2004). [Copyright &y& Elsevier]

In this paper, we investigate the following discrete periodic Lotka-Volterra system with delays: The sufficient and realistic conditions are obtained for the existence of positive periodic solutions and the permanence for the above system. [Copyright &y& Elsevier]

A partial word of length n over a finite alphabet A is a partial map from {0,…, n − 1} into A. Elements of {0,…, n − 1} without image are called holes (a word is just a partial word without holes). A fundamental periodicity result on words due to Fine and Wilf [1] intuitively determines how far two periodic events have to match in order to guarantee a common period. This result was extended to partial words with one hole by Berstel and Boasson [2] and to partial words with two or three holes by Blanchet-Sadri and Hegstrom [3]. In this paper, we give an extension to partial words with an arbitrary number of holes. [Copyright &y& Elsevier]

There are two versions of the Proper Iteration Lemma. The stronger (but less well-known) version can be used to give simpler proofs of iteration theorems (e.g., [7, Lemma 24] versus [9, Theorem IX.4.7]). In this paper we give another demonstration of the fecundity of the stronger version by giving a short proof of Shelah's theorem on the preservation of the ωω-bounding property. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The trust region subproblem plays an important role in optimization and numerical analysis. Many researchers even use it in regularizing ill-posed problems. It appears that the trust region subproblem is ill-posed: the set of solutions is unstable with respect to the data in the functional to be minimized, that is a small error in the functional to be minimized might cause large errors in the set of solutions. The aim of the paper is to study the ill-posed nature of the problem and to suggest methods to overcome the ill-posedness. The methods are mainly based on Tikhonov regularization with the generalized discrepancy principle suggested by Goncharskii, Leonov, and Yagola and the difference of convex functions algorithm (DCA) recently developed by Plant Dinh Tao and Le Thi Hoai An. The open problem of Tikhonov regularization methods for non-linear ill-posed problems how to globally solve non-linear (in general non-convex) optimization problems occurred from them is completely answered for the trust region subproblem by DCA. Several test numerical examples are outlined. [ABSTRACT FROM AUTHOR]

For the problem of minimizing the sum of Euclidean norms (MSN), most existing quadratically convergent algorithms require a strict complementarity assumption. However, this assumption is not satisfied for a number of MSN problems. In this paper, we present a globally and quadratically convergent algorithm for the MSN problem. In particular, the quadratic convergence result is obtained without assuming strict complementarity. Examples without strictly complementary solutions are given to show that our algorithm can indeed achieve quadratic convergence. Preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

In this paper, a mortar finite element method for parabolic problem is presented. Multigrid method is used for solving the resulting discrete system. It is shown that the multigrid method is optional, i.e., the convergence rate is independent of the mesh size L and the time step parameter Τ. [ABSTRACT FROM AUTHOR]

In the present paper, we classify the finite subgroups $G\backslash subset\backslash operatorname\{GL\}\_4(\backslash Bbb\; C)$ such that the quotient $\backslash Bbb\; C^4$ by the action $G$ has only isolated terminal Gorenstein singularities. [ABSTRACT FROM AUTHOR]

In this paper, we improve the Brauer-type inclusion interval and present a modified Brauer-type theorem for singular values. Numerical examples show that our estimation for singular values is more precise than those corresponding results in recent literature. Moreover, we also consider the marginal singular value on the Brauer-type inclusion interval. Some applications of our results are presented. [Copyright &y& Elsevier]

Traditional 'pencil and paper' derivations of the numerical differentiation formulae for f ′[x0] and f″[x0] have been done independently as if there was no connection among the two derivations. This new approach gives a parallel development of the formulae. It requires the solution of a 'linear system' that includes symbolic quantities as coefficients and constants. It is shown how the power of a computer algebra system such as Mathematica can be used to elegantly solve this linear system for f′[x0] and f″[x0]. The extension to derivations of higher order numerical differentiation formulas for the central, forward or backward differences are also presented. [ABSTRACT FROM AUTHOR]

In this paper we define the polyadic Pavelka algebras as algebraic structures for Rational Pavelka predicate calculus (RPL∀). We prove two representation theorems which are the algebraic counterpart of the completness theorem for RPL∀. [ABSTRACT FROM AUTHOR]

In [4] the authors studied the residue field of a model M of IΔ0 + Ω1 for the principal ideal generated by a prime p. One of the main results is that M/ has a unique extension of each finite degree. In this paper we are interested in understanding the structure of any quotient field of M, i.e. we will study the quotient M/I for I a maximal ideal of M. We prove that any quotient field of M satisfies the property of having a unique extension of each finite degree. We will use some of Cherlin's ideas from [3], where he studies the ideal theory of non standard algebraic integers. [ABSTRACT FROM AUTHOR]

This paper suggests a new method, called AINV-A, for constructing sparse approximate inverse preconditioners for positive-definite matrices, which can be regarded as a modification of the AINV method proposed by Benzi and Túma. Numerical results on SPD test matrices coming from different applications demonstrate the robustness of the AINV-A method and its superiority to the original AINV approach. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the iterative solution of ill-conditioned Toeplitz systems generated by continuous nonnegative real-valued functions f with a finite number of zeros. We construct new w-circulant preconditioners without explicit knowledge of the generating function f by approximating f by its convolution f * KN with a suitable positive reproducing kernel KN. By the restriction to positive kernels we obtain positive definite preconditioners. Moreover, if f has only zeros of even order ≤ 2s, then we can prove that the property [This symbol cannot be presented in ASCII format]π-π t2k KN(t)dt ≤ CN-2k (k = 0, … ,s) of the kernel is necessary and sufficient to ensure the convergence of the PCG method in a number of iteration steps independent of the dimension N of the system. Our theoretical results were confirmed by numerical tests. [ABSTRACT FROM AUTHOR]

In this paper, we present a meshless discretization technique for instationary convec- tion-diffusion problems. It is based on operator splitting, the method of characteristics, and a generalized partition of unity method. We focus on the discretization process and its quality. The method may be used as an h-version or a p-version. Even for general particle distributions, the convergence behavior of the different versions corresponds to that of the respective version of the finite element method on a uniform grid. We discuss the implementational aspects of the proposed method. Furthermore, we present the results of numerical examples, where we considered instationary convection-diffusion, instationary diffusion, linear advection, and elliptic problems. [ABSTRACT FROM AUTHOR]

In this paper we describe techniques to represent data which originate from discretization of functions in unstructured meshes in terms of their local scale components. To do so we consider a nested sequence of discretization, which corresponds to increasing levels of resolution, and we define the scales as the ‘difference in information’ between any two successive levels. We obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of numerical schemes by solving for the more compact representation of the numerical solution in terms of its significant scale-coefficients. [ABSTRACT FROM AUTHOR]

We present in this paper numerical simulations of reactive flows interacting with shock waves. We argue that spectral methods are suitable for these problems and review the recent developments in spectral methods that have made them a powerful numerical tool appropriate for long-term integrations of complicated flows, even in the presence of shock waves. A spectral code is described in detail, and the theory that leads to each of its components is explained. Results of interactions of hydrogen jets with shock waves are presented and analyzed, and comparisons with ENO finite difference schemes are carried out. [ABSTRACT FROM AUTHOR]

In this paper we present the convergence analysis of iterative schemes for solving linear systems resulting from discretizing multidimensional linear second-order elliptic partial differential equations (PDEs) defined in a hyperparallelepiped ω and subject to Dirichlet boundary conditions on some faces of ω and Neumann on the others, using line cubic spline collocation (LCSC) methods. Specifically, we derive analytic expressions or obtain sharp bounds for the spectral radius of the corresponding Jacobi iteration matrix and from this we determine the convergence ranges and compute the optimal parameters for the extrapolated Jacobi and successive overrelaxation (SOR) methods. Experimental results are also presented. [ABSTRACT FROM AUTHOR]

This paper gives a quantitative result that if A is a substochastic matrix and has r eigenvalues which are sufficiently close to 1, then A has r disjoint principal submatrices which are nearly stochastic. [ABSTRACT FROM AUTHOR]

This paper extends the author's earlier work which proved that, for a certain class of Hermitian eigenproblems AP = λBP (including, most notably, the Toeplitz eigenproblem), the eigenvectors can be represented as saddlepoints of a special form of the Rayleigh quotient. Each saddlepoint solves a min-max/max-min optimization problem whose optimal value is the eigenvalue. The zeros of the eigenpolynomial factors are located with respect to the unit circle. These results were proved, in part, by using an inertia theorem for Stein equations. For another class of Hermitian eigenproblems AP = λBP, an analogous set of results are derived here using an inertia theorem for Lyapunov equations. In this case, the zeros of the eigenpolynomial factors are located with respect to the imaginary axis, and sufficient conditions for the eigenpolynomial factors to have only extended imaginary zeros are established. The highlight of the article is an important theorem that yields a general factorization of saddlepoint eigenpolynomials and parameterizes all eigenvector saddlepoint representations for an m-dimensional eigenspace. Several key extensions to the theory are also presented. [ABSTRACT FROM AUTHOR]

In this paper we exhibit, under suitable conditions, a neat relationship between the Moore­Penrose generalized inverse of a sum of two matrices and the Moore­Penrose generalized inverses of the individual terms. We include an application to the parallel sum of matrices. [ABSTRACT FROM AUTHOR]

In this paper we consider real or complex skew-Hamiltonian/Hamiltonian pencils λS - H, i.e., pencils where S is a skew-Hamiltonian and H is a Hamiltonian matrix. These pencils occur, for example, in the theory of continuous time, linear quadratic optimal control problems. We reduce these pencils to canonical and Schur-type forms under structure-preserving transformations, i.e., J-congruence-transformations (λS-H) → -JP&ast;J(λS-H)P, where P is nonsingular or unitary. [ABSTRACT FROM AUTHOR]

In this paper we provide an actual bound for the distance between the original and the perturbed right singular vector subspaces of a general matrix with full column rank. We also provide actual relative componentwise bounds for perturbed eigenvectors of a positive definite matrix. [ABSTRACT FROM AUTHOR]

In this paper linear periodic systems of difference equations are classified with respect to periodic similarity and kinematic similarity. Complete sets of invariants of periodic difference equations relative to such similarity transformations are given, and corresponding canonical forms are described. Also the irreducible periodic difference equations, i.e., those that cannot be reduced by such similarities to a nontrivial direct sum, are identified. [ABSTRACT FROM AUTHOR]

Let WN = WN(z1,z2,…,zn) be a rectangular Vandermonde matrix of order n×N, N ≥ n, with distinct nodes zj in the unit disk and zjk-1 as its (j,k) entry. Matrices of this type often arise in frequency estimation and system identification problems. In this paper, the conditioning of WN is analyzed and bounds for the spectral condition numberk2(WN) are derived. The bounds depend on n, N, and the separation of the nodes. By analyzing the behavior of the bounds as functions of N, we conclude that these matrices may become well conditioned, provided the nodes are close to the unit circle but not extremely close to each other and provided the number of columns of WN is large enough. The asymptotic behavior of both the conditioning itself and the bounds is analyzed and the theoretical results arising from this analysis verified by numerical examples. [ABSTRACT FROM AUTHOR]

Superlinear preconditioners (those that provide a proper cluster at 1) are very important for the cg-like methods since they make these methods converge superlinearly. As is well known, for Toeplitz matrices generated by a continuous symbol, many circulant and circulant-like (related to different matrix algebras) preconditioners were proved to be superlinear. In contrast, for multilevel Toeplitz matrices there has been no proof of the superlinearity of any multilevel circulants. In this paper we show that such a proof is not possible since any multilevel circulant preconditioner is not superlinear, in the general case of multilevel Toeplitz matrices. Moreover, for matrices not necessarily Toeplitz, we present some general results proving that many popular structured preconditioners cannot be superlinear. [ABSTRACT FROM AUTHOR]

An exact line search method has been introduced by Benner and Byers [IEEE Trans. Automat. Control, 43 (1998), pp. 101–107] for solving continuous algebraic Riccati equations. The method is a modification of Newton's method. A convergence theory is established in that paper for the Newton-like method under the strong hypothesis of controllability, while the original Newton's method needs only the weaker hypothesis of stabilizability for its convergence theory. It is conjectured there that the controllability condition can be weakened to the stabilizability condition. In this article we prove that conjecture. [ABSTRACT FROM AUTHOR]

In this paper we present three theorems which give insight into the regularizing properties of MINRES. While our theory does not completely characterize the regularizing behavior of the algorithm, it provides a partial explanation of the observed behavior of the method. Unlike traditional attempts to explain the regularizing properties of Krylov subspace methods, our approach focuses on convergence properties of the residual rather than on convergence analysis of the harmonic Ritz values. The import of our analysis is illustrated by two examples. In particular, our theoretical and numerical results support the following important observation: in some circumstances the dimension of the optimal Krylov subspace can be much smaller than the number of the components of the truncated spectral solution that must be computed to attain comparable accuracy. [ABSTRACT FROM AUTHOR]

This paper discusses error spectrum shaping for 2D state-space digital filters. In order to reduce cost by reducing the total number of parameters, a method of analytic design is proposed in which the error feedback coefficient is specified by a diagonal matrix. The proposed algorithm has the feature that the optimal error feedback coefficient can be designed analytically in closed form by minimizing a quadratic form. The validity of the proposed algorithm is demonstrated with a numerical example. The noise reduction effect where the subdecimal part of the optimal coefficient is rounded by the power of 2 is also demonstrated. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 79–90, 1998 [ABSTRACT FROM AUTHOR]

A numerical radius approach is taken in this paper in order to discuss sufficient stability conditions for a well-known family of finite difference schemes for the initial value problem associated with the Petrowski well-posed, multispace-dimensional parabolic system [This symbol cannot be presented in ASCII format] where Apq, Bp, and C are constant matrices, Apq being Hermitian. [ABSTRACT FROM AUTHOR]

The paper presents a hybrid Trefftz (HT) element approach for the numerical solution of transient plate bending problems. In the proposed method, the dynamic plate equation is first discretized with respect to time and then the resulting set of elliptic equations is solved by the corresponding time independent hybrid Trefftz element approach. Two examples are considered to assess the effectiveness of the numerical method. [ABSTRACT FROM AUTHOR]

In this paper a new method has been presented to determine the optimum number of knots for cubic splines. The knot-finding process is based on the numerical integration of the input curve. The number and the location of the knots is determined automatically. The method has been applied to a test case and the performance has been compared with two other existing methods. It is shown that fewer knots are retained for the portions of the curve having small curvature whereas a larger number of knots is retained for highly curved portions. The computer time required by our method depends only upon the number of points in the input curve and does not depend upon the shape of the curve or the desired accuracy. [ABSTRACT FROM AUTHOR]