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Read Online or Download Numerical Methods of Approximation Theory/Numerische Methoden der Approximationstheorie: Workshop on Numerical Methods of Approximation Theory Oberwolfach, September 28–October 4, 1986/Tagung über Numerische Methoden der Approximationstheorie Oberwolfach, PDF
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Extra resources for Numerical Methods of Approximation Theory/Numerische Methoden der Approximationstheorie: Workshop on Numerical Methods of Approximation Theory Oberwolfach, September 28–October 4, 1986/Tagung über Numerische Methoden der Approximationstheorie Oberwolfach,
Example text
O 0 In Section 3, we have mentioned that the interpolation problem with these N sample points is poised. That is, for any given data {fr j , f k0 ' f kn ' fiR. ' fi j , f i j , f i +1 j }, i = 0, ••• , m-l, j o 0 0 0 000 0 0, ••• , 1 n-l, k = O, ••• ,m, and R. = 1, ••• ,n-l, there exists a unique s in S2' satisfying ( 11) J . 1J f ko k 0, ••• ,m S(P kn ) f kn k 0, ••• ,m S(P. ) = f. R. 10 10 R. ) = fio+1R. R. ) 1J S(P ko ) f~ fi j , S(P; j) 0 0 0 0 O, ••• ,n-l fi j , S(Pi +1 j) 0 0 0 0 fi +1 j • 0 0 40 (12) m n I S I a 00 Bo 0 j=-1 lJ lJ i=-1 where x_I < xo ' y-l < Yo' xm+l > xm' Yn+l > Yn' and we fix one coefficient aO 1 2ff 0 - ~(fi 0 +f i +1 0 +f i 0 +1+ f i +10 +1) oJ 0 oJ 0 0 J 0 oJ 0 0 J0 0 1 oJ 0 (This is necessary in view of the linear dependence of Bo 0') 1J By using (2) and all the conformality and smoothing conditions in (2) - (8), we may solve for a i j' i 0 -1 2.
B. 890 angegeben und analog sehr gute EinschlieBungen fUr A2 und A3 • D) Erfahrungen mit Winkeln a n mit '2 < a < n und wurden mit einem Bereich B nach Fig. 8 gesammelt. Man kann das Beispiel als Torsionsproblem interpretieren; entstanden ist es aus dem Temperaturproblem fUr einen dreidimensionalen Raum nach Fig. 8, der im Innern gleichmaBig erwarmt wird mit -~u=1 und am ganzen Rande die Temperatur u=O hat. Mit den in Fig. 8 angegebenen Abmessungen wurde zur Berechnung einer Naherung w (auier Polynomtermen wie bei B) zunachst nur die einspringende Ecke bei P mit Polarkoordinaten r und ~ berUcksichtig und die ausspringendeEcke bei Q noch nicht weiter beachtet.
I 2. i 0 + 1, j 0 1 2. j 2. j 0 + 1 - in terms of the data there. Similarly, the same conformality and smoothing conditions are used to compute the other coefficients, recursively, in terms of the rest of the data values. We have the following recursive formulas. J o [-2Bj 0 f; j 0 0 1 A; +1 B' o Jo 1 [-2A{ +If; j -2Bj f; +1 jo + -ZA{ +If; j 0 ° = 2. • •n - JO o· __ 1_ [4f* BJ'o -k+1 o 0000000 0 and for k 1 + 2" (Bj +A; +2)f; j 2A; f; j ; 0 j -k+1 0 0 0 0 0 0 0 0 + + 42 1 A' B' ;0 jo-k+l [f. '0 jo-k -A' B a ;0 jo-k+l ;0-1 jo-k+l -A B' ;0 jo-k+l a;o jo-k - A; Bj _k+l a; j -k+l] o 0 0 0 for k a; -k o j k IB a.