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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]

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 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 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]

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]

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]

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*J(λS-H)P, where P is nonsingular or unitary. [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]

The spectrum of a first order sentence is the set of all α such that G ( n , n − α ) does not obey zero–one law with respect to this sentence. In this paper, we prove that the minimal number of quantifier alternations of a first order sentence with infinite spectrum equals 3. We have also proved that the spectrum of a first-order sentence with quantifier depth 4 has no limit points except possibly the points 1 ∕ 2 and 3 ∕ 5 . [ABSTRACT FROM AUTHOR]

The basic difference between what may be called curve fitting and what is here called mathematical modeling is that curve fitting is an ad hoc procedure while modeling focuses on the structure of relationships between variables, If one explains observations by curve fitting there is no reason to think that much more than a convenient summarization of data has occurred. Centroids or Gini coefficients for sets of data do not generally explain but summaries. However, coefficients and curves introduced to summaries data often do not remain as uninterpreted summary measures. Introductory material indicated that the paper was to deal with models that are both realistic enough to be of value in research and simple enough for parameters to be estimated. The authors believe that the models presented meet the realism criteria and believe little would be gained by debate on this in the paper. This indicates a need to examine the models to see what kinds of data are critical in distinguishing between the models and seeing that the considerations which could be said to be involved in designing a critical experiment are built into analysis or built into data collection so that there is discrimination between models where this is considered to be necessary or desirable.

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]

Numerical representations of choice functions allow the expression of a problem of choice as a problem of finding maxima of real-valued functions, which requires that less information be defined and which is easier to work with. In this paper, the existence of numerical representations of choice functions by imposing assumptions directly on the choice function is obtained. In particular, it is proved that (IIA) is a necessary and sufficient condition for a choice function to be representable, if the set of alternatives is countable, while the conjunction of (IIA) and a ‘continuity condition’ is sufficient to ensure it in separable topological spaces. [ABSTRACT FROM AUTHOR]

Glazebrook [1] has given an account of improved procedures for strategy evaluation for resource allocation in a stochastic environment. These methods are extended in the paper in such a way that they can be applied to problems which, for example, have precedence constraints and/or an arrivals process of new jobs. Theoretical results, backed up by numerical studies, show that quasi-myopic heuristics often perform well. [ABSTRACT FROM AUTHOR]

In this paper we discuss a general approach to studying asymptotic properties of statistical estimators in stochastic programming. The approach is based on an extended delta method and appears to be particularly suitable for deriving asymptotics of the optimal value of stochastic programs. Asymptotic analysis of the optimal value will be presented in detail. Asymptotic properties of the corresponding optimal solutions are briefly discussed. [ABSTRACT FROM AUTHOR]

This paper develops a new lower bound for single facility location problems with lp distances. We prove that the method produces superior results to other known procedures. The new bound is also computationally efficient. Numerical results are given for a range of examples with varying numbers of existing facilities and p values. [ABSTRACT FROM AUTHOR]

Let G be a continuous life distribution with support [0, c] and consider the following classes of life distributions: e = { F: F(0) = 0 and G -¹F is convex on (0, F[sup-1](l))}, v = (F: G [sup-1]F is concave', on (0, ∞)),L = { F: G[sup-1]F(θx) ≤ θG [sup-1] F(x) for 0 < θ < 1, 0 < x

This paper is an extension of previously published work by Bernard O. Koopman to the general case of any number of tasks and any effect function. A systematic method for the numerical calculation of the maximum effect and its corresponding optimum distribution is presented in a form which is also suitable for solution on an automatic digital computer. For the special case of additive returns which saturate, a special graphical or numerical method for any number of tasks is presented with an example worked out in detail A similar method for multiplicative effects is sketched. [ABSTRACT FROM AUTHOR]

Using approximate, rounded values implies, in a sense, that an exact numerical value may be ignored. In many cases the difference between the exact and approximate values is not important, and replacing exact numbers by their approximate values does not result in undesired consequences. Yet in certain circumstances, rounding significantly influences the solutions of given problems. This is the case, among others, when we allocate indivisible goods. It may happen that the rounding mode affects the result of allocation so much that the rounding differences cannot be neglected by the agents participating in distribution. This paper presents the classic problem of distributing mandates in representative bodies along with different rounding modes in respective solution procedures. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a mixed quadrature rule using Fejer's second rule and Gaussian rule. This rule is taken as the base rule to develop an adaptive integration scheme. Using this scheme, some test integrals have been evaluated. The results are found to be more encouraging as compared to those obtained by using some other quadratures in this integration scheme [ABSTRACT FROM AUTHOR]

The article presents an example of a tricky linear algebra. It states that the trick starts when the instructor writes the number 65 on a paper and the instructor announces his psychic ability to predict sums in advance. Moreover, the numbers from 1-25 are then written consecutively in a 5-by-5 arrangement and a student is asked to choose any five numbers from this with the restriction that no two numbers can lie in the same column or row. It is further instructed that these numbers are then added together by the student before the instructor shows the paper with the number 65 written on it.

This paper is a report on an attempt to teach students in their first and second year of university how to write mathematics. The problems faced by these students are outlined and the system devised to emphasize the importance of communicating mathematics is explained. [ABSTRACT FROM AUTHOR]

Although unconditionally stable (US), the accuracy of ADI-FDTD is not so high as that of conventional FDTD. In this paper, a high-order US-FDTD based on the weighted finite-difference method is presented. A strict analysis of stability shows that it is unconditionally stable. And, more importantly, its numerical-dispersion performance is superior to that of ADI-FDTD. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 142–144, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20749 [ABSTRACT FROM AUTHOR]

This paper is concerned with Wold-type decomposition for regular operators whose orbits under any vector satisfy some growth conditions. Several results on left invertible operators close to isometries are extended. We also give numerous results on the Moore–Penrose inverse for regular operators in this particular setting. [ABSTRACT FROM AUTHOR]

In this paper, we give a formal solution of some nonlinear evolution equations. By the formal solution, we can obtain the blow-up solution of the heat equations, even in the supercritical case. [ABSTRACT FROM AUTHOR]

In multiple-hop MIMO relay systems, an end-to-end channel capacity is restricted by the bottleneck relay. Therefore, in order to obtain the high end-to-end channel capacity, we propose a simple mathematical method to optimize both distances and transmit powers simultaneously. Additionally, the end-to-end channel capacity of optimization based on an one-way and a two-ways transmissions is analyzed. The specific TDMA is proposed to control the transmission of all transmitters on MAC layer and then the distance and the transmit power are optimized based on MAC-PHY cross layer by the proposal particle filter method to obtain the higher end-to-end channel capacity. The calculation result indicates that there is the optimal number of relays that has the maximal end-to-end channel capacity and the trade-off between the end-to-end channel capacity and the delay time. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate how radiality occurs in topological spaces by considering neighbourhood bases generated by nests. We will define a new subclass of radial spaces that contains LOTS, GO-spaces and spaces with well-ordered neighbourhood bases, called the independently-based spaces. We show that first-countable spaces are precisely the independently-based, strongly Fréchet spaces and we give an example of a Fréchet–Urysohn space that is neither independently-based nor strongly Fréchet. [ABSTRACT FROM AUTHOR]