二元混合连分式展开的混合差商极限方法

For a univariate function given by its Taylor series expansion,a continuedfraction expansion can be obtained with the Viscovatov's algorithm,as the limitingvalue of a Thiele interpolating continued fraction or by means of the determinantalformulas for inverse and reciprocal differences with coincident data points.In thispaper,both Viscovatov-like algorithms and Taylor-like expansions are incorporatedto yield bivariate blending continued expansions which are computed as the limitingvalue of bivariate blending rational interpolants,which are constructed based on sym-metric blending differences.Numerical examples are given to show the effectivenessof our methods.     

Wu Wen-tsün Formulae for the Blending of Pipe Surfaces

One of the central questions in CAGD is blending of pipe surfaces. Wu Wen-tsun[1]studied the problem by using the characteristic set method and derived a sufficient andnecessary condition for the existence of a GC1 blending cubic surface of two cylinders whose     

Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.     

CHEBYSHEV METHODS WITH DISCRETE NOISE： THE τ-ROCK METHODS

Stabilized or Chebyshev explicit methods have been widely used in the past to solve stiff ordinary differential equations. Making use of special properties of Chebyshev-like polynomials, these methods have favorable stability properties compared to standard explicit methods while remaining explicit. A new class of such methods, called ROCK, introduced in [Numer. Math., 90, 1-18, 2001] has recently been extended to stiff stochastic differential equations under the name S-ROCK [C. R. Acad. Sci. Paris, 345（10）, 2007 and Commun. Math. Sci, 6（4）, 2008]. In this paper we discuss the extension of the S-ROCK methods to systems with discrete noise and propose a new class of methods for such problems, the τ-ROCK methods. One motivation for such methods is the simulation of multi-scale or stiff chemical kinetic systems and such systems are the focus of this paper, but our new methods could potentially be interesting for other stiff systems with discrete noise. Two versions of the τ-ROCK methods are discussed and their stability behavior is analyzed on a test problem. Compared to the τ-leaping method, a significant speed-up can be achieved for some stiff kinetic systems. The behavior of the proposed methods are tested on several numerical experiments.     

Application of Homotopy Methods to Power Systems

In this paper, the application of homotopy methods to the load flow multi-solution problems of power systems is introduced. By the generalized Bernshtein theorem, the combinatorial number C2n^m is shown to be the BKK bound of the number of isolated solutions of the polynomial system transformed from load flow equations with generically chosen coefficients. As a result of the general Bezout number, the number of paths being followed is reduced significantly in the practical load flow computation. Finally, the complete P-V cures are obtained by tracking the load flow with homotopy methods.     

A HIGHLY ACCURATE NUMERICAL METHOD FOR FLOW PROBLEMS WITH INTERACTIONS OF DISCONTINUITIES

1. IntroductionCompared with the widely used shock capturing methods for the compressible flows, theshock fitting methods have the main advantage of accuracy. The shock fitting methods areusually very accurate wherever it can be applied. Several kinds of shock fitting methods havebeen developed il1 the last tl1ree decades. Glimrn and his coworkers have worked extensively onthe front tracking methods and applied them to many complicated problems with shocks andother types of singularities [1]-[…     

Block Based Bivariate Blending Rational Interpolation via Symmetric Branched Continued Fractions

This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.     

Predictor-Corrector Smoothing Methods for Monotone LCP

In this paper, we analyze the global and local convergence properties of two predictor-corrector smoothing methods, which are based on the framework of the method in [1], for monotone linear complementarity problems (LCPs). The difference between the algorithm in [1] and our algorithms is that the neighborhood of smoothing central path in our paper is different to that in [1]. In addition, the difference between Algorithm 2.1 and the algorithm in [1] exists in the calculation of the predictor step. Comparing with the results in [1],the global and local convergence of the two methods can be obtained under very mild conditions. The global convergence of the two methods do not need the boundness of the inverse of the Jacobian. The superlinear convergence of Algorithm 2.1‘ is obtained under the assumption of nonsingularity of generalized Jacobian of Φ(x,y) at the limit point and Algorithm 2.1 obtains superlinear convergence under the assumption of strict complementarity at the solution. The efficiency of the two methods is tested by numerical experiments.     

粘弹性波动方程的H~1-Galerkin混合有限元方法误差估计(英文)

H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.     

A class of globally convergent conjugate gradient methods

Conjugate gradient methods are very important ones for solving nonlinear optimization problems, especially for large scale problems. However, unlike quasi-Newton methods, conjugate gradient methods were usually analyzed individually. In this paper, we propose a class of conjugate gradient methods, which can be regarded as some kind of convex combination of the Fletcher-Reeves method and the method proposed by Dai et al. To analyze this class of methods, we introduce some unified tools that concern a general method with the scalar βk having the form of φk/φk-1. Consequently, the class of conjugate gradient methods can uniformly be analyzed.     

非线性弹性理论的混合能量形式广义变分原理

本文首先对弹性材料的应变能函数∑(E_ij)和余应能函数∑C(S_ij)的部分“对应”变量作Legendre变换,引进“对应”的混合余应变能函数∑_klC和混合应变能函数∑_kl。进而,给出非线性弹性理论的各种“对应”的混合能量形式广义变分原理。线性弹性理论也有相应结果,它是本文结果的特殊情况。     

Ritz-Galerkin approximations in blending function spaces

Summary This paper considers the theoretical development of finite dimensional bivariate blending function spaces and the problem of implementing the Ritz-Galerkin method in these approximation spaces. More specifically, the approximation theoretic methods of polynomial blending function interpolation and approximation developed in [2, 11–13] are extended to the general setting of L-splines, and these methods are then contrasted with familiar tensor product techniques in application of the Ritz-Galerkin method for approximately solving elliptic boundary value problems. The key to the application of blending function spaces in the Ritz-Galerkin method is the development of criteria which enable one to judiciously select from a nondenumerably infinite dimensional linear space of functions, certain finite dimensional subspaces which do not degrade the asymptotically high order approximation precision of the entire space. With these criteria for the selection of subspaces, we are able to derive a virtually unlimited number of new Ritz spaces which offer viable alternatives to the conventional tensor product piecewise polynomial spaces often employed. In fact, we shall see that tensor product spaces themselves are subspaces of blending function spaces; but these subspaces do not preserve the high order precision of the infinite dimensional parent space.Considerable attention is devoted to the analysis of several specific finite dimensional blending function spaces, solution of the discretized problems, choice of bases, ordering of unknowns, and concrete numerical examples. In addition, we extend these notations to boundary value problems defined on planar regions with curved boundaries.     

Reconstruction of linear functionals on classes of analytic functions of two variables on the basis of generalized information

For classes of analytic functions defined in terms of the two-dimensional Hadamard composition, we propose a renewal method for linear functionals based on blending constructions. The best renewal methods are indicated, and the exact estimates of errors are given.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 32–37, January, 1993.     

BOUNDARY PENALTY FINITE ELEMENT METHODS FOR BLENDING SURFACES,I BASIC THEORY

1.IntroductionBlendingsurfacesissaidifwhentwoframesurfaces(orbodies)arelocatedalreadyjasmoothlytransferringsurfaceissoughttoconnectthetwoframesurfacesalongcertainboundary.Usually,theterminology"smoothness"meansthattheblendingsurfacebelongstogeometriccontinuityCI(Foleyetal.(90)[14),i.e.,theblendingsurfaceanditstangentplanearecontinuousuntilthejointboundary.Manyliteraturesarereportedonthissubject.Wemerelymentionafewofthemrelevanttothispaper.Uniforml)Thi.workwassupportedbytheresearchgrantsfromt…     

Boundary penalty finite element methods for blending surfaces,III. Superconvergence and stability and examples

This paper is Part III of the study on blending surfaces by partial differential equations (PDEs). The blending surfaces in three dimensions (3D) are taken into account by three parametric functions, x(r,t),y(r,t) and z(r,t). The boundary penalty techniques are well suited to the complicated tangent (i.e., normal derivative) boundary conditions in engineering blending. By following the previous papers, Parts I and II in Li (J. Comput. Math. 16 (1998) 457–480; J. Comput. Appl. Math. 110 (1999) 155–176) the corresponding theoretical analysis is made to discover that when the penalty power σ=2, σ=3 (or 3.5) and 0<σ⩽1.5 in the boundary penalty finite element methods (BP-FEMs), optimal convergence rates, superconvergence and optimal numerical stability can be achieved, respectively. Several interesting samples of 3D blending surfaces are provided, to display the remarkable advantages of the proposed approaches in this paper: unique solutions of blending surfaces, optimal blending surfaces in minimum energy, ease in handling the complicated boundary constraint conditions, and less CPU time and computer storage needed. This paper and Li (J. Comput. Math. 16 (1998) 457–480; J. Comput. Appl. Math.) provide a foundation of blending surfaces by PDE solutions, a new trend of computer geometric design.     

A class of piecewise interpolating functions based on barycentric coordinates

Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolant function by means of polynomial pieces and ensure that some regularity conditions are guaranteed at the break-points. In this work, we propose a novel class of piecewise interpolating functions whose expression depends on the barycentric coordinates and a suitable weight function. The underlying idea is to specialize to the 1D settings some aspects of techniques widely used in multi-dimensional interpolation, namely Shepard’s, barycentric and triangle-based blending methods. We show the properties of convergence for the interpolating functions and discuss how, in some cases, the properties of regularity that characterize the weight function are reflected on the interpolant function. Numerical experiments, applied to some case studies and real scenarios, show the benefit of our method compared to other interpolant models.     

Boundary penalty finite element methods for blending surfaces, . Superconvergence and stability and examples

This paper is Part III of the study on blending surfaces by partial differential equations (PDEs). The blending surfaces in three dimensions (3D) are taken into account by three parametric functions, x(r,t),y(r,t) and z(r,t). The boundary penalty techniques are well suited to the complicated tangent (i.e., normal derivative) boundary conditions in engineering blending. By following the previous papers, Parts I and II in Li (J. Comput. Math. 16 (1998) 457–480; J. Comput. Appl. Math. 110 (1999) 155–176) the corresponding theoretical analysis is made to discover that when the penalty power σ=2, σ=3 (or 3.5) and 0<σ1.5 in the boundary penalty finite element methods (BP-FEMs), optimal convergence rates, superconvergence and optimal numerical stability can be achieved, respectively. Several interesting samples of 3D blending surfaces are provided, to display the remarkable advantages of the proposed approaches in this paper: unique solutions of blending surfaces, optimal blending surfaces in minimum energy, ease in handling the complicated boundary constraint conditions, and less CPU time and computer storage needed. This paper and Li (J. Comput. Math. 16 (1998) 457–480; J. Comput. Appl. Math.) provide a foundation of blending surfaces by PDE solutions, a new trend of computer geometric design.     

成品油调合优化模型及其应用研究

为了提高炼油厂制定成品油调合方案的科学性。研究建立成品油调合优化问题的非线性规划模型。首先从不同的层次，分析提出炼油厂成品油调舍工作的三类优化问题；其次，研究给出三类成品油调合优化问题的非线性规划模型形式；再次，针对成品油调合优化模型形式的特点，提出相应的求解技术；最后，通过在某炼油厂的一个应用实例验证上述成品油调合优化模型的有效性。     

A Practical Application of Linear Programming in the Mining Industry

The paper describes the application of linear programming to the allocation of coking coals from twenty-eight collieries to seven central washeries and blending plants in one N.C.B. area. The problem, which is of the simplex type, is reduced to the transportation form. Some details are given of the production method, implementation of the linear programming model and the follow-up.