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71.
Wilhelm Niethammer 《Numerische Mathematik》1980,34(3):271-283
Summary A nonlinear generalizationÊ
z
of Euler's series transformation is compared with the (linear) Euler-Knopp transformationE
z
and a twoparametric methodE
. It is shown how to applyE
orE
, to compute the valuef(zo) of a functionf from the power series at 0 iff is holomorphic in a half plane or in the cut plane. BothE
andE
, are superior toÊ
z
. A compact recursive algorithm is given for computingE
andE
,. 相似文献
72.
Harry Yserentant 《Numerische Mathematik》1980,34(2):171-187
Summary Difference methods for the numerical solution of linear partial differential equations may often be improved by using a weighted right hand side instead of the original right hand side of the differential equation. Difference formulas, for which that is possible, are called Mehrstellenformeln or Hermitian formulas. In this paper the Hermitian formulas for the approximation of Laplace's operator are characterized by a very simple condition. We prove, that in two-dimensional case for a Hermitian formula of ordern at leastn+3 discretization points are necessary. We give examples of such optimal formulas of arbitrary high-order. 相似文献
73.
Jutta Weisel 《Numerische Mathematik》1980,35(2):201-222
Summary In this note we consider so called p-analytic mappings of simply or doubly connected domains on rectangles or circular rings. Real and imaginary parts of the mappings can be described by minimal-principles. By minimizing the corresponding functionals in a class of linear or bilinear finite elements we obtain an approximation of the mapping and also upper and lower bounds for the p-module of a domain with polygonal boundary. Error bounds are given for smooth and for piecewise constant functionsp. We present numerical experiments. 相似文献
74.
Claus Schneider 《Numerische Mathematik》1980,35(1):35-43
Summary For the numerical evaluation of
, 0<<1 andx smooth, product integration rules are applied. It is known that high-order rules, e.g. Gauss-Legendre quadrature, become normal-order rules in this case. In this paper it is shown that the high order is preserved by a nonequidistant spacing. Furthermore, the leading error terms of this product integration method and numerical examples are given. 相似文献
75.
Summary The method of nondiscrete mathematical induction is applied to a multistep variant of the secant method. Optimal conditions for convergence as well as error estimates, sharp in every step, are obtained. 相似文献
76.
D. J. Harfiel 《Numerische Mathematik》1980,35(3):355-359
Summary LetPQ ben×n real matrices so that ifPAQ for some matrixA, thenA is nonsingular. Letp andq ben-dimensional real column vectors. This paper determines the set of all solutionsx to the equationAx=b for allA andb so thatPAQ andpbq. 相似文献
77.
Summary We consider the problem of studying the behaviour of the eigenvalues associated with spline functions with equally spaced knots. We show that they are
wherem is the order of the spline andn, the number of knots.This result is of particular interest to prove optimality properties of the Generalized Cross-Validation Method and had been conjectured by Craven and Wahba in a recent paper. 相似文献
78.
In the presence of a Lewis acid the phenol-Passerini three-component reaction (phenol-P-3CR) system is found to deliver a product of the phenol-Ugi four-component reaction (phenol-U-4CR). It is the first demonstration of an isocyanide as an amine equivalent in isocyanide-based multicomponent reactions (IMCRs). In general, by using Ti(O-i-Pr)4 in MeOH both phenol-U-4CR and U-4CR products are synthesized from an aromatic aldehyde, a phenolic or carboxylic acid, and an isocyanide. Moreover, by using MeCN as the solvent, the phenol-P-3CR products can be obtained in good yields without contamination of the phenol-U-4CR products. 相似文献
79.
Summary This paper is devoted to the numerical analysis of a bidimensional two-phase Stefan problem. We approximate the enthalpy formulation byC
0 piecewise linear finite elements in space combined with a semi-implicit scheme in time. Under some restrictions related to the finite element mesh and to the timestep, we prove positivity, stability and convergence results. Various numerial tests are presented and discussed in order to show the accuracy of our scheme.This work is supported by the Fonds National Suisse pour la Recherche Scientifique. 相似文献
80.
Martin Kütz 《Numerische Mathematik》1982,39(3):421-428
Summary Let
, be holomorphic in an open disc with the centrez
0=0 and radiusr>1. LetQ
n
(n=1, 2, ...) be interpolatory quadrature formulas approximating the integral
. In this paper some classes of interpolatory quadratures are considered, which are based on the zeros of orthogonal polynomials corresponding to an even weight function. It is shown that the sequencesQ
n
9f] (n=1, 2, ...) are monotone. Especially we will prove monotony in Filippi's quadrature rule and with an additional assumption onf monotony in the Clenshaw-Curtis quadrature rule. 相似文献