Dianxuan Gong

Inverse Eigenvalue Problem for Real Symmetric Five-Diagonal Matrix

In this paper, a kind of inverse eigenvalue problem which is the reconstruction of real symmetric five-diagonal matrix by there different eigenpairs is proposed. Given there distinguished eigenpairs, using the special computational relationship of Jacobi matrix and symmetric five-diagonal matrix, the solvability of the problem is discussed, and the sufficient and necessary conditions for the existence of a solution of this problem, as well as the analytic formula of this solution, are derived. Furthermore, to prove the theory, an appropriate numerical experiment is given by programming.

An Adaptive Method for Choosing Center Sets of RBF Interpolation

Radial basis functions (RBF) provide powerful meshfree methods for multivariate interpolation for scattered data. RBF methods have been praised for their simplicity and ease of implementation in multivariate scattered data approximation. But both the approximation quality and stability depend on the distribution of the center set. It leads immediately to the problem of finding good or even optimal point sets for the reconstruction process. Many methods are constructed for center choosing. In this paper, we give a short overview of these algorithms including thinning algorithm, greedy algorithm, arclength equipartition like algorithm and k-means clustering algorithm. A new adaptive data-dependent method is provided at the end with some numerical examples to show its effectiveness.

Duplicate form of gould-hsu inversions and binomial identities

It is well known that inversion techniques have an important role in the development of combinatorial identities. In 1973, Gould and Hsu [6] offered a pair of surprising inverse series relations. Then it was utilized by Chu [3, 4] to study systematically hypergeometric series identities. By applying the duplicate form of Gould-Hsu inversions to a terminating 4 F3 −series identity form Saalscutzs theorem, we shall establish a family of binomial identities implying numerous interesting hypergeometric series identities.

Summation formulae for q-Watson type 4ϕ3-series

Abstract We use the method of series rearrangement to establish two families of summation formulae for q -Watson type 4 ϕ 3 -series in this paper.

The construction of transition surface between nonadjacent bicubic T-B spline surfaces

We get the expression of cubic T-B spline curve. Further more, it derives the expression of bicubic T-B spline surface in tensor product form. Based on the geometric continuous connection theory between surfaces, we construct a transition surface between two nonadjacent bicubic T-B spline surfaces. Then discuss smooth connect conditions between nonadjacent bicubic T-B spline surfaces and transition surface, At last, we calculate the relations among the three control points matrixes in these cases.

Adaptive methods for center choosing of radial basis function interpolation: a review

Radial basis functions provide powerful meshfree method for multivariate interpolation for scattered data. But both the approximation quality and stability depend on the distribution of the center set. Many methods have been constructed to select optimal center sets for radial basis function interpolation. A review of these methods is given. Four kinds of center choosing algorithms which are thinning algorithm, greedy algorithm, arclength equipartition like algorithm and k-means clustering algorithm are introduced with some algorithmic analysis.

Computer simulation of fuzzy comprehensive evaluation and its application in water quality evaluation

The water quality assessment is an important basis for implementing water pollution control planning. In this paper, we use fuzzy comprehensive evaluation method to build a mathematical model of the Yangtze River Water Quality Assessment. Finally we find the method to solve the water pollution situation of the Yangtze River by comprehensive evaluation. We seek the model solving by computer simulation.The key problems are focused on the following two issues: (1) Makeing a comprehensive quantitative evaluation of Yangtze River water quality in the past two years and analyzing the water pollution situation in various regions. (2) Researching, analysising the permanganate index of major pollutants over the Yangtze River for nearly a year and ammonia nitrogen source is mainly in what areas.

Properties of Planar Triangulation and Its Application

Further research will be done on triangulation partitions. particularly, more careful analysis is made on even triangulation of simply connected domain, and a number of new properties are obtained. Using these new properties, some proof of the theorems on graph theory become easy and simple. For example, using the property an arbitrary planner even triangulation can be expressed as the union of a number of disjoint star domains, one can easily prove the equivalence of the three statement triangulation is even, triangulation is 3-vertex signed and triangulation is 2-triangle signed.

q -Extensions of Gauss’ Fifteen Contiguous Relations for 2 F 1 -Series

Contiguous relation is a fundamental concept within the theories of hypergeometric series and orthogonal polynomials. Gauss’ fifteen contiguous relations imply that any three 2 F 1-series whose corresponding parameters differ by integers are linearly related. As q-extensions of hypergeometric series, basic hypergeometric series are used widely in Statistics and Physics. By the method of comparing coefficients, we establish fifteen interesting three-term relations for 2 φ 1-series. Their limiting cases recover Gauss’ fifteen contiguous relations for 2 F 1-series.

Some practice and ideas on education reform of numerical analysis course

As a required course in polytechnic schools, “Numerical Analysis” is the bridge between the practical application and mathematic theories. Based on the course features and some problems encountered in the teaching process, we carried out some research on education reforms, and put forward some ideas on teaching content and teaching methods. All these achieved good results in teaching practice.