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By Richard Bellman (auth.), John Ll. Morris (eds.)

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Additional info for Conference on Applications of Numerical Analysis: Held in Dundee/Scotland, March 23–26, 1971

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A = {~IP g L, lPiCx) I ~ 1 n [ i=1 JiCv) = Max pgA pp x ¢ ~, n fO #i[x] Oi v[x)dx = ~ i=I i = 1 ..... 3. < 1 pp x g ~) i=1 it(v) = fa [oi v(x)l Max i=1, .... On peut construire en sjoutant de nouveaux la contrainte Nous d o n n e r o n s dx n un s e u l exemples& Pi[x)~O partir des pr@c@dents pp x e ~ , i = I ..... n. example. 4. < I • Pi on m o n t r e = S~ (x) qua Max i:1, .... i v[x))+dx. p. x e ~, i=I ..... 1. UNE PREMIERE u du probl~me ; l'id~e directrice une suite X destin~e & approm nous construisons une suite dual, u = F - S~X et enfin nous montrons que u m m m vers la solution u du probl~me primal.

On peut construire en sjoutant de nouveaux la contrainte Nous d o n n e r o n s dx n un s e u l exemples& Pi[x)~O partir des pr@c@dents pp x e ~ , i = I ..... n. example. 4. < I • Pi on m o n t r e = S~ (x) qua Max i:1, .... i v[x))+dx. p. x e ~, i=I ..... 1. UNE PREMIERE u du probl~me ; l'id~e directrice une suite X destin~e & approm nous construisons une suite dual, u = F - S~X et enfin nous montrons que u m m m vers la solution u du probl~me primal. METHODE I1 s'agit de i'adaptation autre que la m~thode probl~me dual.

14) I n = 0,I,2,... Wn+ 1 = H2(Wn,Vn) starting with the elements Vo,W o g D. 3) are satisfied and that the operator T is completely continuous. 15) v 1•uKw I . 16) u(x) = T u ( x ) = ~o u 1 + tulxIt dt 1+x I we can choose Hj(~,:) = H(~,:) = ~o 1+t ~ (x) 1+x :(t) dt . I For Vo= O, Wo= 2 we get v1= I+2---~and w1= 2. 16) has at least one solution u(x) with I -I~ ~ u(x) ~ 2 . ,a q. A. with restrictions). 2) 0 i Gj(x,a) , g= Min. ,m , for x cB, a ~A. This is a generalization of the approximation problems with restricted ranges (Taylor [69], Schumaker [69~ 48 5.

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