منابع مشابه
On Smoothest Interpolants *
This paper is concerned with the problem of characterizing those functions of minimum LP-norm on their nth derivative, <=p=<, that sequentially take on the given values (ei). For p = the unique minimizing function is characterized. For p < fairly explicit necessary conditions are given.
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(1) inf{‖f ‖p : f ∈ C [0, 1], f(ti) = ei, i = 1, . . . , m}, where ‖ · ‖p is the usual L [0, 1] norm, 1 ≤ p ≤ ∞, and to characterize f for which the above infimum is attained. If m ≤ n, then this problem has a simple solution. There are algebraic polynomials of degree at most n−1 satisfying the interpolation data, and any of these polynomials obviously solve our problem. If m > n then, in gener...
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It is known that random k-SAT formulas with at least (2 · ln 2) ·n random clauses are unsatisfiable with high probability. This result is simply obtained by bounding the expected number of satisfying assignments of a random k-SAT instance by an expression tending to 0 when n, the number of variables tends to infinity. This argument does not give us an efficient algorithm certifying the unsatisf...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1949
ISSN: 0003-4851
DOI: 10.1214/aoms/1177729956