Jincai Chang

The research on parallel least squares curve fitting algorithm

In many ways about solving the large overdetermined system of linear equations, the serial algorithm is much more complex. However, the parallel method of least squares curve fitting, which refers to in the paper starting from the parallel technology, improves the computing efficiency, reduces the time loss and provides a new approach and a new ideas in order to solve the super-set of linear equations of the study. Firstly, this paper introduces the keystone about the method of least squares curve fitting and the fundamental method of parallel computing, and establishes a master-slave model of the parallel method of least squares curve fitting in the basic of the method least squares. Secondly, though elaborated the parallel fitting algorithm, it gives the reader an intuitive understanding of and citing a specific example to verify the feasibility of the algorithm, which shows the superiority of the method and effectiveness.

Construction of Transition Curve between Nonadjacent Cubic T-B Spline Curves

In this paper, we investigate the geometric continuous connection between the adjacent cubic T-B spline curves, and the construction of transition curve between nonadjacent T-B spline curves. First, we calculate the expression of cubic T-B spline basis function and the expression of cubic T-B spline curve. Then based on the condition of smooth connection between adjacent cubic T-B spline curves, we construct the relations of control points between transition curve and nonadjacent T-B spline curves. Thus we get the geometric continuous connect conditions between transition curve and nonadjacent T-B spline curves.

Computer simulation of the grey system prediction method and its application in water quality prediction

The water quality prediction is an important basis to implement water pollution control programs. In this paper, the gray system method is used to build a mathematical model of water quality prediction for the Yangtze River and using computer to simulate it to complete the implementation of the method for solving the model. Finally we find the method to solve problem of predicting the water quality of Yangtze River. The key problems are focused on the following two issues. (1) If we do not take more effective control measures, we make prediction analysis of the future development trendbased on past data. (2). According to the prediction analysis, we use computer to simulate that how much sewage we need to address each year.

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.

Teaching reform research of mathematics analysis courses

The Current problems of the mathematics analysis courses in science and engineering colleges and universities is unsatisfactory. Peoples traditional concepts of mathematical analysis courses need to be updated. This article discussed the teaching content and method of Mathematical analysis and Put forward suggestions for improvement, such as Mathematical culture and numerical experiments bring in teaching, etc.

The design and practice of numerical analysis teaching platform

Numerical analysis is an important basis of science and engineering professional courses in higher education system. The course not only can train the thinking ability in mathematics, but also be able to train students to apply scientific methodology and computer technology to analyze and solve practical problems. Based on the teaching practice in the past decade, we have made the multi-level researches and reform on the teaching mode, teaching content, teaching methods and so on. The multi-dimensional teaching platform which can effectively support series of numerical analysis courses gradually formed. This article focuses on introducing the multi-dimensional design and teaching practice of the platform.

Numerical algorithm research for nonlinear ODEs and stability analysis in computer

This paper discussed numerical algorithm of the initial and boundary value problem of nonlinear ordinary differential equations and analysis its stability in computer. The iterated algorithm with spline function for initial value problem in nonlinear ordinary differential equations was studied. Based on the principle of Newtons algorithm for nonlinear equation, a parallel algorithm for initial value problems in nonlinear ordinary differential equations is constructed and then analysis the stability of this method . It shows that the methods have high precision and quick convergence speed and good stability.

Analysis of 2D intrinsic mode function

The definition of 2D IMF is very important for bidimensional empirical mode decomposition of images. V. Vatchev analyzed 1D IMF in his doctoral dissertation, and introduced the concept of weak-IMF which point out that the solution of Sturm-Liouville equations can be regarded as 1D weak-IMF. In this paper we try to give the definition of 2D IMF and investigate the relations between the vibration theory of thin plate and 2D IMF. Three types of bivariate splines with certain mechanical meanings can be defined as 2D weak-IMF.

A new noise aided method for random data analysis

The Empirical Mode Decomposition(EMD) is a simple and effective sifting process which can decompose complicated data set into Intrinsic Mode Functions (IMFs). But neither the origin EMD nor its recent progress considered the randomness of data sufficiently. In this paper, random splines are introduced as a new approximation tool for random data analysis. According to the randomness of data itself, we present Random Empirical Mode Decomposi-tion (REMD) to decompose random data set into Random Intrinsic Mode Functions (RIMFs).

Application of parallel Newton interpolation in dew-point detection of low humidity area

On Newton interpolation has been studied theoretically deduced combination with parallel idea in this paper, to get an improved parallel-Newton interpolation. And it gives a speedup and efficiency theoretically. Finally put its application in the dew-point detection of low humidity area among the areas with low humidity environment, the capacitive dew-point sensors measure the frequency and the dew-point by showing the value of the non-linear relationship, parallel-Newton interpolation, the actual measured against a group of data have been calculated the traditional Newton-interpolation and the improved results of a parallel-Newton interpolation were compared, analysis of parallel speedup and efficiency of the method shows the superiority of the method and effectiveness. To provide a new approach, new ideas to solve the function problem, that does not facilitate the processing or computing.