By Z. Ciesielski (auth.), Juan Alfredo Gómez-Fernandez, Francisco Guerra-Vázquez, Guillermo López-Lagomasino, Miguel A. Jiménez-Pozo (eds.)
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Extra info for Approximation and Optimization: Proceedings of the International Seminar held in Havana, Cuba, Jan. 12–16, 1987
4; the feasible set M(t) gives is shaded. rise to two 51 k l/l/: t >_ ~ (x I .... ,Xk) /~ 2 x. n - i=l ~ Xk+ I ..... n) From Fig. 4 we occurrement see that % value t < 0, k = n - 1 a the of a local minimum. m a x i m u m has a functional J ~ 4. only x j=k+l t < 0, k = 0 Fig. 2 ~ b situation Moreover, of f which of Fig. b gives rise to note that the c o r r e s p o n d i n g is less than the value the local at the local minimum. Case II : 6 < O. Now, k must be equal satisfy the number of positive to 1 or n.
Therefore the turbation KnXn . Kn Our aim is to determine, f o r . Since the spectrum is closed in DUn(K) I~ • llKn . depends upon the s p e c i f i c norm induce the same topology on on This norm may be d i f f e r e n t from the o p e r a t o r norm rK(A ) induced by Jl • I]Kn Un(K ) ~ 0 and HDII = rK(A ) . 4) KnXn formulas f o r the s t a b i l i t y r a d i u s , the norm I I . il on KnXn has M • ]IKn . ll be a norm on p a t < b l Kn w i t h (C I) flAx llKn H • IIKn Kn . if A norm II • II on Kn×n is said to be s t r o n g l y the f o l l o w i n g two c o n d i t i o n s are s a t i s f i e d _< 1 1 A l l .
D h + Z ~jDxg j x i•l I x i . h. iEl i i ~ ~ jEjo(~ ) jgj' the numbers A. 3). e. V, X I, Dxgj(E) ~ = where V is 0' a j • matrix J O (z)). whose Now J columns X (n-vectors) form a basis for T(x). e. D2L(z)V, cf. ). X The set E is pieced together from one-dimensional C2-manifolds and it is the closure of the set of all points of Type i; moreover, constitute a discrete basic degeneracies the points of Type 2-5 subset of E. The points of Type 2-5 represent (compare also the interesting paper ).
Approximation and Optimization: Proceedings of the International Seminar held in Havana, Cuba, Jan. 12–16, 1987 by Z. Ciesielski (auth.), Juan Alfredo Gómez-Fernandez, Francisco Guerra-Vázquez, Guillermo López-Lagomasino, Miguel A. Jiménez-Pozo (eds.)