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1.
It is shown that the CaratheodoryFejer extension of afinite geometric series can be given explicitly up to a simplepolynomial equation in an auxiliary variable. This result allowsus to analyse the Caratheodory-Fejer approximation method inthe case where the quotients of successive Maclaurin coefficientsof the given function tend to a limit.
*Research carried out while this author was at ETH Zurich partiallysupported by a Royal Society European Visiting Fellowship. 相似文献
2.
Mixed block elimination for linear systems with wider borders 总被引:1,自引:0,他引:1
The paper is about the stable solution of possibly ill-conditionedbordered linear systems. Given stable solvers for matrix A andfor AT, we prove that the Govaerts Mixed Block Elimination (BEM)method constitutes a stable solver for the matrix consistingof A or AT with a border of width 1, and hence by recursionfor a border of any width. We express the algorithm in an efficient,iterative, form. We analyse its operation count, and verifythe theory by extensive numerical experiments.
*Senior Research Associate of the Belgian National Fund of ScientificResearch NFWO. 相似文献
3.
We propose a method for the approximation of analytic functionson Jordan regions that is based on a CarathéodoryFejértype of economization of the Faber series. The method turnsout to be very effective if the boundary of the region is analytic.It often still works when the region degenerates to a Jordanarc. We also derive related lower and upper bounds for the errorof the best approximation.
*Research carried out while this author was at ETH Zurich partiallysupported by a Royal Society European Visiting Fellowship. 相似文献
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In a recent paper Fox & Mayers discuss the numerical solutionof implicit ordinary differential equations of the form f(x,y(x), y'(x)) = 0. They find that numerical methods can be veryunreliable near the point where fy' = 0. In this paper we givea theoretical analysis of the problem which enables us to explainwhen to expect numerical difficulties. We suggest a possibleline of approach for the solution of such problems, and discusssome numerical examples.
Research supported by the National Science Foundation, the Officeof Naval Research, the Army Research, and the Air Force Officeof Scientific Research. Travel funding provided by the Universityof Toronto and the British Council. 相似文献
6.
We prove that a family of methods for the numerical solutionof the Kortewegde Vries equation is convergent. Thisfamily includes as particular cases some known finite differenceand finite element schemes. It is also found that the stabilityproperties of the methods vary significantly with the treatmentof the non-linear term.
On leave from Shanghai University of Science and Technology,Shanghai, China. 相似文献
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Optimal recovery using thin plate splines in finite volume methods for the numerical solution of hyperbolic conservation laws 总被引:4,自引:0,他引:4
The theory of optimal recovery is applied to finite volume methodsfor the numerical solution of conservation laws in multiplespace dimensions. Classical polynomial EN0 (essentially non-oscillatory)algorithms can be interpreted as trivial recovery operatorsfor the point functional in the light of this theory. Thin platesplines are identified as optimal recovery functions in Beppo-Levispaces and can be seen as multi-dimensional analogues of cubicsplines. Recovery algorithms of ENO-type based on thin platesplines are developed and applied to test problems includingthe Euler equations of compressible gas dynamics.
E-mail: Thomas.Sonar{at}ts.go.dlr.de 相似文献
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On the perturbation of LU and Cholesky factors 总被引:1,自引:0,他引:1
In a recent paper, Chang and Paige have shown that the usualperturbation bounds for Cholesky factors can systematicallyoverestimate the errors. In this note we sharpen their resultsand extend them to the factors of the LU decomposition. Theresults are based on a new formula for the first-order termsof the error in the factors.
* This report is available by anonymous ftp from thales.cs.umd.eduin the directory pub/reports. 相似文献
11.
Nicaise Serge; Witowski Katharina; Wohlmuth Barbara I. 《IMA Journal of Numerical Analysis》2008,28(2):331-353
12.
In this paper we analyze the use of a combined Nystrm and finite-elementprocedure for approximating the scattered time-harmonic acousticfield produced when an incident wave interacts with a boundedinhomogeneity. The coupling technique uses a smooth artificialboundary and explicitly decouples the integral equation andfinite-element computations. We prove convergence of the method.One highlight of this analysis is that we prove Sobolev spaceerror estimates for the Nystrm scheme (which is usually analyzedin Hlder spaces). We also present some numerical results.
E-mail: kirsch{at}am.uni-erlangen.de
E-mail: monk{at}math.udel.edu 相似文献
13.
The theory of the 1-inverse of a matrix is used to derive allsymmetric updates which satisfy a matrix equation. This generalsolution is then used to obtain the solution which is minimumin a symmetrically weighted Frobenius norm. The minimum normsolution can be used to derive the minimum norm updates usedin quasi-Newton methods for unconstrained optimization.
This research was supported in part by NIH Grant No. AM17593. 相似文献
14.
Conditions which ensure the applicability of extrapolation-in-timeof the backward-difference Galerkin and CrankNicolsonGalerkin methods for linear parabolic initial-boundary problemsare discussed. Deferred correction and defect correction proceduresfor these discrete-time Galerkin methods are formulated andtheir theoretical properties summarized. These procedures yieldapproximations which are up to fourth-order correct in time,and whose computation requires less work per time step thanthat required by extrapolation. The results of numerical experiments,which demonstrate the expected rates of convergence with respectto the time discretization of the various techniques, are presented.
*The work of this author was supported in part by the NationalScience Foundation under grant MCS-8102295 相似文献
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Adaptive frame methods for elliptic operator equations: the steepest descent approach 总被引:2,自引:0,他引:2
Dahlke Stephan; Raasch Thorsten; Werner Manuel; Fornasier Massimo; Stevenson Rob 《IMA Journal of Numerical Analysis》2007,27(4):717-740
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Arnal Josep; Migallon Violeta; Penades Jose; Szyld Daniel B. 《IMA Journal of Numerical Analysis》2008,28(1):143-161
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Bai Xiaoming; Yang Xiao-Song; Li Huimin 《IMA Journal of Mathematical Control and Information》2007,24(4):483-491
19.
Permanent address: Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794. Of concern here are the GaussChebyshev formulae for numericalsolution of singular integral equations of the Cauchy-type.The coefficient matrix of the linear sustem of algebraic equationscorresponding to the dominant term term is shown to have aninverse, which is expressed in a neat, closed form. Using thenorm of the inverse matrix, the effect of quadrature errorson the computed solution is estimated. Using Jackson's theoremson "best approximation", convergence of the procedure is provedunder favourable conditions. In the course of analysis, a numberof identities involving the zeros of Chebyshev polynomials offirst and second kind is obtained.
*Dedicated to Professor I. N. Sneddon on his sixty-third birthday. 相似文献
20.
Using the technique of singlar perturbation, a procedure fordesigning a discretetime reducedorder controllerfor robust stabilization is proposed. The theoretical aspectsare derived directly from the results of the generalized PopovYakubovichtheory recently developed.
1Vlad Ionescu, 3 Emile Zola, Bucharest, 71272, Romania.
2Cristian Oara, 34 Austrului, Bucharest, 73115, Romania. 相似文献