PROBLEMS AND METHODS IN MATRIX VALUED RATIONAL INTERPOLATION

A variety of matrix rational interpolation problems include the partial realizationproblem for matrix power series and the minimal rational interpolation problem for generalmatrix functions.Several problems in circuit theory and digital filter design can also be re-duced to the solution of matrix rational interpolation problems[1—4].By means of thereachability and the observability indices of defined pairs of matrices,Antoulas,Ball,Kang and Willems solved the minimal matrix rational interpolation problem in[1].On

On Approximation by Two Kinds Modified Durrmeyer Rational Interpolation Operators in Lω^M Spaces

This paper discusses the approximation problem of two kinds Durrmeyer rational interpolation operators in Orlicz spaces with weight functions,and gives a kind of Jackson type estimation of approximation order by means of continuous modulus, Hardy-Littlewood maximal function, convexity of N function and Jensen inequality.

A New Method of Constructing Bivariate Vector Valued Rational Interpolation Function

At present,the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions.In order to get vector valued rational interpolation function with lower degree and better approximation effect,the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d 1 (0 ≤ d 1 ≤ m) and d 2 (0 ≤ d 2 ≤ n),builds bivariate polynomial vector interpolation for each piece,then combines with them properly.As compared with previous methods,the new method given by this paper is easy to compute and the degree for the interpolants is lower.

On Newman-Type Rational Interpolation to |x| at the Adjusted Chebyshev Nodes of the Second Kind

Recently Brutman and Passow considered Newman-type rational interpolation to |x| induced by arbitrary sets of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods,one could establish the exact order of approximation for some special nodes.In the present note we consider the sets of interpolation nodes obtained by adjusting the Chebyshev roots of the second kind on the interval [0,1] and then extending this set to [-1,1] in a symmetric way.We show that in this case the exact order of approximation is O( 1 n 2 ).

TRIANGULAR C^m INTERPOLATION BY RATIONAL FUNCTIONS

Two general local Cm triangular inter polation schemes by rational functions from Cm data are proposed for any nonnegative integer m. The sohemes can have either 2m+1 order algebraic precision if the required data are given on vertices and edges, or m+E[m/2]+1 or m+1 order algebraic precision if the data are given only at vertices. The orders of the inter error are estimated. Examples that show the correctness and effectiveness of the scheme are presented.

BIVARIATE BLENDING RATIONAL INTERPOLANTS

Bath the Newton inter polating polynomials and the Thiele-type inter polating continued fractions based on inverse differences are used to construct a kind of blending rational inter polants and an error estimation is grven.

Further study of rubber-like elasticity: elastic potentials matching biaxial data

By virtue of the rational interpolation procedure and logarithmic strain, a direct approach is proposed to obtain elastic potentials that exactly match uniaxial data and shear data for elastomers. This approach reduces the determination of multiaxial elastic potentials to that of two one-dimensional potentials, thus bypassing usual cumbersome procedures of identifying a number of unknown parameters. Predictions of the suggested potential are derived for a general biaxial stretch test and compared with the classical data given by Rivlin and Saunders(Rivlin, R. S. and Saunders, D. W. Large elastic deformation of isotropic materials. VII: experiments on the deformation of rubber. Phill. Trans. Royal Soc. London A, 243, 251–288(1951)). Good agreement is achieved with these extensive data.

High-precision stress determination in photoelasticity

Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics.The numerical error resulting from the stress determination is a main concern as it is always a function of parameters in discretization.To improve the accuracy of stress calculation,a novel meshless barycentric rational interpolation collocation method(BRICM)is proposed.The derivatives of the shear stress on the calculation path are determined by using the differential matrix which converts the differential form of the equations of equilibrium into a series of algebraic equations.The advantage of the proposed method is that the auxiliary lines,grids,and error accumulation which are commonly used in traditional shear difference methods(SDMs)are not required.Simulation and experimental results indicate that the proposed meshless method is able to provide high computational accuracy in the full-field stress determination.