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Get Numerische Methoden der Approximationstheorie/Numerical PDF

By P. M. Anselone, J. W. Lee (auth.), L. Collatz, H. Werner, G. Meinardus (eds.)

ISBN-10: 3034876920

ISBN-13: 9783034876926

ISBN-10: 3764308249

ISBN-13: 9783764308247

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Read Online or Download Numerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory: Vortragsauszüge der Tagung über numerische Methoden der Approximationstheorie vom 25. bis 31. Mai 1975 im Mathematischen Forschungsinstitut Oberwolfach (Schwarzwald) PDF

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Extra info for Numerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory: Vortragsauszüge der Tagung über numerische Methoden der Approximationstheorie vom 25. bis 31. Mai 1975 im Mathematischen Forschungsinstitut Oberwolfach (Schwarzwald)

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In this paper we are emphasizing the geometry and algebra of blending function methods, not their analysis. 9), the function precision implies that it would be more reasonable to let '(x,y) be a cubic interpolant, along the relevant "sectionsli, that is, 56 BAIUmlLL p(x,O) =F(x,O) = ~O(X)F(O,O) + ~1/3(X)F(1/3,O) + ~z/3(X)F(z/3,O) + ~1(X)F(1,O) ete. The resulting interpolant eubic polynomials. 8: Cubie diseretisation of bilinearly blended eoons pateh. 3, we eould eonsider a pieeewise bilinearly blended Boolean sum on h by h squares with cubie diseretisations of the transfinite data.

7) is an example of a discretisation. (Pi $ P2)F is called a (rectangular) Coons patch. In connexion with finite element analysis, Gordon [22] 53 BARNHILL oalls it a transfinite element. (Pi Ef) P2 )F is also caUed a blending f'unction interpolant. 3). The three interpolants PtPzF, P,F (and PzF), and (p, e Pz)F form a lattioe in which P,P z is algebraically "minimal", P, am Pz interme die. te, aIld P, Ef) Pz "maximal", in Gardon 's [21] terminology. Also, P,P z =PzP, above, but, as we ahall see, thia is not true, in general, for interpolanta on nonreotangular regions.

2: Boundary and interior curves. 3: Discrete deta given at tne x pomts. 2. 1: Univariate Linear Interpolant. 1) f( 0) ____________ f( 1 ) + ... o 1 The data are the "positions" f(O) and f(1). The weighting functions (1-x) and x are called the IIblending" functions for these data. Historically, bivariate schemes have been built up from univariate schemes, usually by means of tensor products. 2) This funetion is linearly ruled along parallels to the two eoordinate axes. 2: Tensor p roduet Bilinear Interpolant.

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Numerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory: Vortragsauszüge der Tagung über numerische Methoden der Approximationstheorie vom 25. bis 31. Mai 1975 im Mathematischen Forschungsinstitut Oberwolfach (Schwarzwald) by P. M. Anselone, J. W. Lee (auth.), L. Collatz, H. Werner, G. Meinardus (eds.)


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