Spline methods for a Birkhoff interpolation problem

In this paper, we study two new spline methods for the Birkhoff interpolation problem proposed in Costabile and Longo (Calcolo 47:49–63, 2010). Our methods are based on cubic spline and quintic spline respectively. The new methods are easy to be implemented. They are effective not only in approximating the original function but also in approximating its derivatives. The respective remainders and error bounds are given. Numerical tests are performed. Numerical results confirm the theoretical analysis and show that our methods are very practical.     

A time-varying Beurling-Lax theorem and a related interpolation problem

This article concerns linear time-varying interpretations of the Beurling-Lax-Ball-Helton theorem and of Sarason's interpolation problem. The former characterizes shift-invariantH ₂ (Krein) subspaces. Unilateral shift invariance reflects both causality and time invariance. Removing the stationarity requirement, a generalized theorem provides a characterization of certain causal subspace families M_t L₂(t, ), t . Sarason's interpolation problem is interpreted here as a search for a (close to) minimal induced norm system, given causal input-output specifications. The Beurling-Lax theorem helps in identifying admissible specification classes. The problem is then reduced to and solved in terms of a linear time-varying Nehari problem. Technically, developments are based on timedomain, state-space methods.This research was supported by the National Science Foundation and by the Army Research Office.     

On the scalar rational interpolation problem

A new technique is derived for determining a parametrization of all minimal complexity rational functionsa(x)/b(x) interpolating an arbitrary sequence of points. Complexity is measured in terms of max{deg(a), deg(b) +r } wherer is an arbitrary integer (so thatr=0 corresponds to the McMillan degree). Our construction uses Gröbner bases of submodules of the free module of rank 2 over the polynomial ring in one variable and extends previous work on the key equation of error control coding theory.     

Nevanlinna-Pick interpolation problem for two frequency scalesystems

The Nevanlinna-Pick interpolation problem for a parametric set of data is considered. Sufficient conditions are obtained that guarantees a two frequency scale solution. Decomposition of the problem into two Nevanlinna-Pick interpolation problems with smaller data size is presented. An algorithm is developed which computes the solution as the result of combining the solutions for these two smaller problems     

General variational approach to the interpolation problem

The Talmi and Gilat variational approach to the interpolation problem in arbitrary dimension is presented together with the corresponding physical model. The connection of this approach to some known spline methods is demonstrated and new interpolation functions are derived for one-, two- and three-dimensional cases. They are designed to be flexible through the use of meaningful parameters and to give good approximations of both the function itself and its derivatives as well.     

Construction and application of fractal interpolation surfaces

Fractal geometry has unique advantages for a broad class of modeling problems, including natural objects and patterns. This paper presents an approach to the construction of fractal surfaces by triangulation. After introducing the notion of iterated function systems (IFSs), we prove theoretically that the attractors of this construction are continuous fractal interpolation surfaces (FISs). Two fast, parallel, and iterative algorithms are also provided. Several experiments in natural phenomena simulation verify that this method is suitable for generating complex 3D shapes with self-similar patterns.Project supported by the National Natural Science of China     

The subspace Nevanlinna interpolation problem and the most powerful unfalsified model

A generalization of the tangential Nevanlinna interpolation problem will be studied from a behavioral point of view. Necessary and sufficient conditions for its solvability and a characterization of all its solutions are derived. These results are obtained by associating to the interpolation data a behavior that enjoys a special structure.     

A knowledge-based problem solving method in GIS application

Model design for theme analysis is one of the biggest challenges in GIS. Many real applications in GIS require functioning not only in data management and visualization, but also in analysis and decision-making. Confronted with an application of planning a new metro line in a city, a typical GIS is unable to accomplish the task in the absence of human experts or artificial intelligence technologies. Apart from being models for analyzing in different themes, some applications are also instances of problem solving in AI. Therefore, in order to strengthen its ability in automatic analysis, many theories and technologies from AI can be embedded in the GIS. In this paper, a state space is defined to formalize the metro line planning problem. By utilizing the defined state evaluation function, knowledge-based rules and strategies, a heuristic searching method is developed to optimize the solutions iteratively. Experiments are implemented to illuminate the validity of this AI-enhanced automatic analysis model of GIS.     

A quasilinearization algorithm and its application to a manipulator problem

A quasilinearization algorithm is proposed for the computation of optimal control of a class of constrained problem. The constraints are inequality constraints on functions of the state and control variables, and bounds on the values of the control variables. Necessary conditions for optimal control of the control problem are derived. In the iterative procedure, no prior information is required regarding the sequence of constrained and unconstrained arcs and the inequality constraints which are on their boundaries along a specific constrained arc of the optimal trajectory. All this information will be determined within the iterative procedure using some necessary conditions for optimal control. The ability of the proposed algorithm to solve practical problems is demonstrated by its application to several variations of two problems, one of which is a common manipulator problem in industry where transportation of open vessels of liquid is to be performed in a specified period of time. It is shown that the proposed quasilinearization algorithm is an effective tool in deriving optimal control policies for a common type of manipulator operation in industry.     

三层并行遗传算法及装箱问题中的应用

提出了一个新的基于线程构建模块(TBB)的三层并行遗传算法(TPGA)。与传统遗传算法相比,在保证了算法正确性的前提下提高了运行效率,并将遗传算法的数据编码、任务处理和数据解码分别进行并行化,提高了收敛速度。TBB是Intel提供的能够完整表现并行性的代码库。采用C++语言实现了基于TBB的TPGA和串行遗传算法(SGA),通过大量实验证明,TPGA同SGA相比,不但提高了收敛速度,而且能够取得一致的最优解。     

Graph isomorphism and theorems of Birkhoff type

Computing - Two graphsG andG′ having adjacency matricesA andB are called ds-isomorphic iff there is a doubly stochastic matrixX satisfyingXA=BX.Ds-isomorphism is a relaxation of the classical...     

Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is designed so that normalization problems of high analytical complexity could be solved. It is used to obtain the Birkhoff normal form of the Hamiltonian in the given problem. The normalization is carried out up to the 6th order of expansion of the Hamiltonian in the coordinates and momenta. Analytical expressions for the coefficients of the normal form of the 6th order are derived. Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format. The analogue of the Deprit formula for the stability criterion is derived in the 6th order of normalization. The obtained floating-point numerical values for the normal form coefficients and the stability criterion confirm the results by Markeev (1969) and Coppola and Rand (1989), while the obtained analytical and exact numeric expressions confirm the results by Meyer and Schmidt (1986) and Schmidt (1989). The given computational problem is solved without constructing a specialized algebraic processor, i.e., the designed computer algebra package has a broad field of applicability.     

多模糊条件的知识推理方法的应用

针对多模糊条件问题,提出一种基于模糊逻辑与神经元网络相结合的解决方法,同时以一个具体的系统为例,叙述了解决问题的流程。     

A discrete monotonous interpolation scheme

An algorithm for the problem of transforming a regular array of tabular points into a monotonous array of tabular points is presented.     

A semantic approach to interpolation

Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially generalize known interpolation results; all the others are new. We also discuss some applications of our results to the theory of institutions and of algebraic specifications, and a Craig–Robinson version of these results.     

A self-tuning neuromorphic controller: application to the crane problem

This paper is concerned with the design and application of a self-tuning controller, aided by means of neural networks (NN). The structure of the controller is based on the use of neural networks as an implicit self-tuner for the controller. The aim of this approach is to take advantage of the learning properties of the neural networks to increase the performance of the self-tuning. The application of this technique is performed on an overhead crane. The control objective is to suppress undesirable oscillations during operation of the crane. First, some simulations were carried out, as well as a comparison with a standard self-tuning method, that demonstrate the advantages of this method. After this, a real-time implementation on a scale prototype of a crane was done to verify the applicability of the method.     

LMIs for constrained polynomial interpolation with application in trajectory planning

We consider an open-loop trajectory planning problem for linear systems with bound constraints originating from saturations or physical limitations. Using an algebraic approach and results on positive polynomials, we show that this control problem can be cast into a constrained polynomial interpolation problem admitting a convex linear matrix inequality (LMI) formulation.