منابع مشابه
On constrained extrema
Assume that I and J are smooth functionals defined on a Hilbert space H. We derive sufficient conditions for I to have a local minimum at y subject to the constraint that J is constantly J(y). The first order necessary condition for I to have a constrained minimum at y is that for some constant λ, I ′ y +λJ ′ y is identically zero. Here I ′ y and J ′ y are the Fréchet derivatives of I and J at ...
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We study the complexity of one-dimensional extrema testing: given one input number, determine if it is properly contained in the interval spanned by the remaining n input numbers. We assume that each number is given as a finite stream of bits, in decreasing order of significance. Our cost measure, referred to as the leading-input-bits-cost (or LIB-cost for short), for an algorithm solving such ...
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We present a new approach to model edges in monochrome images. The method is divided in two parts: the localization of possible edge points and their valuation. The first part is based on the theory of minimal paths, where the selection of an energy and a set of sources determines a partition of the domain. Then, the valuation is obtained by the creation of a contrast driven hierarchy of partit...
متن کاملExtrema of graph eigenvalues
In 1993 Hong asked what are the best bounds on the k’th largest eigenvalue λk(G) of a graph G of order n. This challenging question has never been tackled for any 2 < k < n. In the present paper tight bounds are obtained for all k > 2, and even tighter bounds are obtained for the k’th largest singular value λk(G). Some of these bounds are based on Taylor’s strongly regular graphs, and other on ...
متن کاملClassifying extrema using intervals
We present a straightforward and verified method of deciding whether the point x ∈ R, n > 1, such that ∇f(x) = 0, is the local minimizer, maximizer or just a saddle point of a real-valued function f . The method scales linearly with dimensionality of the problem and never produces false results.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1970
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(70)80083-7