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Finally we also briefly compare with other relaxation techniques including interval extensions and αBB relaxations.
We reformulate here the transition rules using the interval extensions of the regulation functions.
Finally, we construct interval extensions of RS to rigorously draw independent and identically distributed samples from small phylogenetic tree spaces.
Such functions have well-defined interval extensions that satisfy inclusion isotony and exact range enclosure, i.e. range(f; x ) = f(x ).
Although the three distinct expressions f(x), f'(x) and f"(x) of the real function f: ℝ ↦ ℝ of Example 1 are equivalent upon evaluation in the reals, their respective interval extensions f(x ) = [0, 0], f'(x ) = x × [0, 0], and f"(x ) = x - x are not.
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The first takes advantage of optimization theory, while the second is based on interval extension.
The technique used in the optimization is an interval extension based on a Taylor expansion of the objective function.
Even more efficiently, using interval extension from interval mathematics, the generalized interval eigenvalue problem may be divided into two generalized eigenvalue problems for real symmetric matrix pairs.
The understanding of fatigue variability in turbine engine materials is vital to permit a reduction of US Air Force sustainment costs through fatigue life extension and/or inspection interval extension.
Combining the interval extension of function with the perturbation theory of dynamic response, the method for interval dynamic response analysis is derived.
To deal with data set in the form of a number of intervals, the interval extension evaluation method (IEEM) has been previously introduced.
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