Interpolation between sequence transformations

Levin's sequence transformation [1] and a structurally very similar sequence transformation [4] behave quite differently in convergence acceleration and summation processes. In particular, it was found recently that Levin's transformation fails completely in the case of the strongly divergent Rayleigh-Schrödinger and renormalized perturbation expansions for the ground state energies of anharmonic oscillators, whereas the structurally very similar sequence transformation gives very good results [14,17]. For a more detailed investigation of these phenomena, a sequence transformation is constructed which — depending on a continuous parameter — is able to interpolate between Levin's transformation and the other sequence transformation. Some numerical examples, which illustrate the properties of the interpolating sequence transformation, are presented.     

Extensions of Levin's transformations to vector sequences

Levin's transformations are extended to vector sequences. Convergence theorems for certain linear and certain logarithmic vector sequences are proved. Numerical examples are also given.     

On a generalization of the Richardson extrapolation process

Summary A convergence result for a generalized Richardson extrapolation process is improved upon considerably and additional results of interest are proved. An application of practical importance is also given. Finally, some known results concerning the convergence of Levin's T-transformation are reconsidered in light of the results of the present work.     

高振动积分的一种新的有效Levin-type配置法

本文给出了高振动积分的一种新的有效Levin-type配置法, 并对它的有效性和精度进行了检验, 与Levin配置法相比较, 这种方法具有更高的精度而且容易实现.     

A special case of de Branges' theorem on the inverse monodromy problem

We give a new proof of a special case of de Branges' theorem on the inverse monodromy problem: when an associated Riemann surface is of Widom type with Direct Cauchy Theorem. The proof is based on our previous result (with M.Sodin) on infinite dimensional Jacobi inversion and on Levin's uniqueness theorem for conformal maps onto comb-like domains. Although in this way we can not prove de Branges' Theorem in full generality, our proof is rather constructive and may lead to a multi-dimensional generalization. It could also shed light on the structure of invariant subspaces of Hardy spaces on Riemann surfaces of infinite genus.This work was supported by the Austrian Founds zur Förderung der wissenschaftlichen Forschung, project-number P12985-TEC     

Quasipower and hypergeometric series — construction and evaluation

It is proved that some power series converging very slowly in a neighbourhood of the point 1 can be transformed intoquasipower series. The latter converge faster but are more complicated because they contain some hypergeometric series₂ F ₁. Standard methods of the values evaluation for needed hypergeometric series with the aid of recurrence relations are not sufficiently efficient for some variable values. Therefore a new method, formally similar to Levin's transforms, is proposed. More generally, this is a method of approximative evaluating of such a solution of an inhomogeneous recurrence relation of order one which has some particular asymptotic properties.The efficacity of the proposed methods is analyzed in detail for Euler's dilogarithm. This is a typical function whose power series is approached with difficulties ifz1. In particular, its Padé approximants are sufficiently accurate only for, sayx[–1, 1/2]. Hermite-Padé approximation is more effective. Resulting irrational approximants generalize in some sense partial sums of the quasipower series introduced here.     

用非线性方程组求解等式约束非线性规划问题的降维算法

本文研究线性和非线性等式约束非线性规划问题的降维算法.首先,利用一般等式约束问题的降维方法,将线性等式约束非线性规划问题转换成一个非线性方程组,解非线性方程组即得其解;然后,对线性和非线性等式约束非线性规划问题用Lagrange乘子法,将非线性约束部分和目标函数构成增广的Lagrange函数,并保留线性等式约束,这样便得到一个线性等式约束非线性规划序列,从而,又将问题转化为求解只含线性等式约束的非线性规划问题.     

Explicit Traveling Wave Solutions to Nonlinear Evolution Equations

First of all, some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations, nonlinear dissipative dispersive wave equations, nonlinear convection equations, nonlinear reaction diffusion equations and nonlinear hyperbolic equations, respectively.     

一类模糊非线性方程组及解法

模糊非线性方程组 ,在模糊控制和现实生活中很普遍 .本文考虑一类模糊非线性方程组的性质 ,然后给出一种解法 .首先把模糊非线性方程组转变成非线性规划 ,再用非线性规划中的方法或软件来解 .