On the approximate computation of certain strongly singular integrals

Finite-part integrals, first introduced by Hadamard in connection with hyperbolic partial differential equations, have been found useful in a number of engineering applications. In this paper we investigate some numerical methods for computing finite-part integrals with a double-pole singularity.     

Two adaptive Gauss-Legendre type algorithms for the verified computation of definite integrals

We propose a two algorithms for computation of (sharp) enclosures of definite interevals: alocal adaptive algorithm (LAA) and aglobal adaptive algorithm (GAA). Both algorithms are based on Gauss-Legendre quadrature. Error terms are bounded using automatic differentiation in combination with interval evaluations. Several numerical examples are presented; these examples include comparison with an adaptive interval Romberg scheme.     

Runtime and language support for compiling adaptive irregular programs on distributed-memory machines

In many scientific applications, arrays containing data are indirectly indexed through indirection arrays. Such scientific applications are called irregular programs and are a distinct class of applications that require special techniques for parallelization. This paper presents a library called CHAOS, which helps users implement irregular programs on distributed-memory message-passing machines, such as the Paragon, Delta, CM-5 and SP-1. The CHAOS library provides efficient runtime primitives for distributing data and computation over processors; it supports efficient index translation mechanisms and provides users high-level mechanisms for optimizing communication. CHAOS subsumes the previous PARTI library and supports a larger class of applications. In particular, it provides efficient support for parallelization of adaptive irregular programs where indirection arrays are modified during the course of computation. To demonstrate the efficacy of CHAOS, two challenging real-life adaptive applications were parallelized using CHAOS primitives: a molecular dynamics code, CHARMM, and a particle-in-cell code, DSMC. Besides providing runtime support to users, CHAOS can also be used by compilers to automatically parallelize irregular applications. This paper demonstrates how CHAOS can be effectively used in such a framework. By embedding CHAOS primitives in the Syracuse Fortran 90D/HPF compiler, kernels taken from the CHARMM and DSMC codes have been automatically parallelized.     

A remark on the numerical computation of improper integrals

In this note a transformation is given reducing improper integrals to integrals with smooth integrands. The transformation may be represented in terms of elementary functions and is easily applicable in connection with standard mathematical software for the numerical evaluation of integrals with smooth integrands.     

An approximate nonmyopic computation for value of information

It is argued that decision analysts and expert-system designers have avoided the intractability of exact computation of the value of information by relying on a myopic assumption that only one additional test will be performed, even when there is an opportunity to make large number of observations. An alternative to the myopic analysis is presented. In particular, an approximate method for computing the value of information of a set of tests, which exploits the statistical properties of large samples, is given. The approximation is linear in the number of tests, in contrast with the exact computation, which is exponential in the number of tests. The approach is not as general as in a complete nonmyopic analysis, in which all possible sequences of observations are considered. In addition, the approximation is limited to specific classes of dependencies among evidence and to binary hypothesis and decision variables. Nonetheless, as demonstrated with a simple application, the approach can offer an improvement over the myopic analysis     

On approximate computation of the quantile criterion

We propose a method for computing the quantile criterion with given accuracy based on the use of converging sequences of two-sided approximations to the probabilistic criterion. The method is applied to solving the estimation problem for a given quantile level for the distribution of the norm of a two-dimensional Gaussian vector with correlated components.     

On the convergence of some quadrature rules for Cauchy principal-value and finite-part integrals

In this paper sufficient conditions are derived to ensure the convergence of the Elliott and Hunter types of quadrature rules for the evaluation of weighted Cauchy principal-value integrals of the form: The simultaneous convergence in the interval (?1, 1) of both quadratures was established for a class of Hölder-continuous functionsf(f∈H _μ ). Corrections of some previous statements on the subject of convergence of such quadratures are also included. Moreover, a simple derivation of the Hunter and Elliott types of quadrature rules for the evaluation of the derivative of thep-th-order of the abovestated integral was given and sufficient conditions for the convergence of the Hunter-type quadrature were obtained. Thus, the convergence of this integral was ensured for functionsf such thatf ^(p) ∈H _μ .     

Exact and approximate computation of B-spline curves on surfaces

Curves on surfaces are important elements in computer aided geometric design. After presenting a method to explicitly compute these curves in three-dimensions, practical algorithmic issues are discussed concerning the efficiency of the implementation. Good approximations are important because of the quite high degree of exact curves on surfaces. We present two approximate solutions to the problem. The first is derived from the exact representation, while the second extends conventional least-squares approximation by incorporating the geometry of the surface as well. The efficiency and behaviour of the algorithms are evaluated by means of examples.     

Data management for a class of iterative computations on distributed-memory MIMD systems

The paper discusses data management techniques for mapping a large data space onto the memory hierarchy of a distributed memory MIMD system. Experimental results for structural biology computations using the Molecular Replacement Method are presented.     

On the computation of high order Rys quadrature weights and nodes

We develop and describe a new method for computing Gaussian quadrature weights and nodes for non-classical weight functions and apply it to the Rys quadrature used to accurately compute two-electron repulsion integrals over Gaussian type orbitals in molecular electronic structure theory. With the new method, using an ordinary 64 bit floating point representation, it is possible to compute weights and nodes to an accuracy of one part in 10¹² even for the absurdly high value of N=101$N=101$.     

多关系实体链计算与近似连接查询的研究

针对多个实体集关系,提出了链接属性及实体链有关概念,研究发现了具有相同或相似链接属性的实体链计算方法.多关系之间的实体链计算是近似连接查询的关键,该研究通过分析链接属性相似度,解决多关系之间数据冲突问题,设计了2-实体链和k-实体链计算算法,并运用扩展的SQL查询语言实现实体链计算的主要过程.实体链能够应用于多关系高效查询及动态查询,而且可以获得较高的查询准确率.     

Intelligence computation based on adaptive tracking design for a class of non-linear discrete-time systems

In this article, a direct adaptive neural networks control algorithm is presented for a class of SISO discrete-time systems with non-symmetric dead-zone. The property of the dead-zone is discretized. Mean value theorem is used to transform the systems into a special form. The unknown functions in the input–output model are approximated using the radial basis function neural networks. Compared with the results for the discrete non-symmetric dead-zone, this article presents a new algorithm to reduce the computational burden. Lyapunov analysis method is utilized to prove that all the signals in the closed-loop systems are semi-global uniformly ultimately bounded. The tracking error is proved to converge to a small set around the zero. A simulation example provided to illustrate the effectiveness of the control schemes.     

Fast computation of close-coupling exchange integrals using polynomials in a tree representation

The semi-classical atomic-orbital close-coupling method is a well-known approach for the calculation of cross sections in ion–atom collisions. It strongly relies on the fast and stable computation of exchange integrals. We present an upgrade to earlier implementations of the Fourier-transform method.For this purpose, we implement an extensive library for symbolic storage of polynomials, relying on sophisticated tree structures to allow fast manipulation and numerically stable evaluation. Using this library, we considerably speed up creation and computation of exchange integrals. This enables us to compute cross sections for more complex collision systems.

Program summary

Program title: TXINTCatalogue identifier: AEHS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHS_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 12 332No. of bytes in distributed program, including test data, etc.: 157 086Distribution format: tar.gzProgramming language: Fortran 95Computer: All with a Fortran 95 compilerOperating system: All with a Fortran 95 compilerRAM: Depends heavily on input, usually less than 100 MiBClassification: 16.10Nature of problem: Analytical calculation of one- and two-center exchange matrix elements for the close-coupling method in the impact parameter model.Solution method: Similar to the code of Hansen and Dubois [1], we use the Fourier-transform method suggested by Shakeshaft [2] to compute the integrals. However, we heavily speed up the calculation using a library for symbolic manipulation of polynomials.Restrictions: We restrict ourselves to a defined collision system in the impact parameter model.Unusual features: A library for symbolic manipulation of polynomials, where polynomials are stored in a space-saving left-child right-sibling binary tree. This provides stable numerical evaluation and fast mutation while maintaining full compatibility with the original code.Additional comments: This program makes heavy use of the new features provided by the Fortran 90 standard, most prominently pointers, derived types and allocatable structures and a small portion of Fortran 95. Only newer compilers support these features. Following compilers support all features needed by the program.

• • 

  GNU Fortran Compiler “gfortran” from version 4.3.0

• • 

  GNU Fortran 95 Compiler “g95” from version 4.2.0

• • 

  Intel Fortran Compiler “ifort” from version 11.0

Running time: Heavily dependent on input, usually less than one CPU second.References:

• [1] 

  J.-P. Hansen, A. Dubois, Comput. Phys. Commun. 67 (1992) 456.

• [2] 

  R. Shakeshaft, J. Phys. B: At. Mol. Opt. Phys. 8 (1975) L134.

     

Computing fourier integrals by means of near-optimal quadrature rules of the Lagrangian type

As shown inGustafson-Dahlquist [3] the computation of a large class of slowly convergent Fourier integrals can be cast into the problem of evaluating a certain Stieltjes integral over the interval [0, 1]. If the integrator can be shown to be non-decreasing, generalized Gauss rules can be used but this calls for the solution of a generally ill-conditioned non-linear system. In this paper we report experimental results, which illustrate the fact, that if the abscissae are chosen according to a simple strategy and then the weights are computed from a linear system, the resulting rules of Lagrangian type are almost optimal in a certain sense.     

Synthesis of controllers for target problems of hybrid systems using approximate computation

This paper presents methodologies based on approximate computations for the target control problem of hybrid systems modelled by hybrid automata. The problem of backward reachability and its relation to the control synthesis is studied using approximate analysis techniques. The reachability operators, considering non-linear and linear dynamics with affine disturbances, are under-approximated using state space discretization that involves hyper-cubes. The timing information provided by the backward reachability computation is used in order to design a sub-optimal controller. The computational techniques are applied to the batch evaporator benchmark process which has practical interest.     

Global adaptive tracking for a class of nonlinear time-delay systems

This paper aims to extend the newly developed global adaptive regulation scheme to adaptive tracking for a general class of nonlinear systems with both parameter uncertainties and unknown time delay for all the system states. With a simple yet novel decomposition of some coupling functions derived from the introduction of a reference signal, a backstepping tracking control strategy is proposed which possesses the feature that for each design step, a dynamic gain is introduced to generate an additional term to counteract the system nonlinearities and parameter uncertainties. As a result, a memoryless adaptive state-feedback controller is obtained to achieve the global adaptive tracking.     

Global adaptive stabilization for a class of feedforward nonlinear systems

In this note, we solve the global adaptive stabilization problem for a class of feedforward nonlinear systems which possesses a much more general feedforward structure than those feedforward nonlinear systems which can be globally adaptively stabilized previously. The design of our adaptive stabilizer takes a two-step procedure: we first design a stabilizer containing a certain tuning parameter and then design a switching logic to tune it online in a switching manner. Global stability results of the closed-loop system have been proved, and a simulation example is given.     

Algorithms based on difference equations of infinite order and the computation of Laplace-type integrals

Certain processes in analysis, e. g., the computation of Laplace-Stieltjes moment integrals, lead to difference equations of infinite order. In this paper, we seek to apply an analog of the famous Miller algorithm for difference equations of finite order to these systems. In certain situations we are able to demonstrate the convergence of the algorithm.     

Efficient computation of adaptive threshold surfaces for image binarization

The problem of binarization of gray level images, acquired under non-uniform illumination is reconsidered. Yanowitz and Bruckstein proposed to use for image binarization an adaptive threshold surface, determined by interpolation of the image gray levels at points where the image gradient is high. The rationale is that high image gradient indicates probable object edges, and there the image values are between the object and the background gray levels. The threshold surface was determined by successive over-relaxation as the solution of the Laplace equation. This work proposes a different method to determine an adaptive threshold surface. In this new method, inspired by multiresolution approximation, the threshold surface is constructed with considerably lower computational complexity and is smooth, yielding faster image binarizations and often better noise robustness.