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Re: modal intervals

Svetoslav Markov wrote:


 a*x=1 is  solvable for all nonzero Kaucher intervals a,
and the solution is alpha*dual (a), where alpha is a real
number:

alpha = 1/(a^-a^+) in inf/sup presentation a=[a^-, a^+]
here dual [a^-, a^+] = [a^+, a^-], resp. dual (a';a") = (a'; -a")


If I apply this to a=[-1,1], which is nonzero, I get
    x = alpha*dual(a)=(-1)*[1,-1] = [1,-1]
which satisfies
    a*x = [1,-1]*[-1,1] = [0,0]
So it is not a solution.


Arnold Neumaier