Not Polynomial

Views Updated: Dec 15, 2025

Abbreviation

Pronunciation

/nɑt ˌpɑˌliˈnoʊmiəl/

The author study the minimum cost flow problem with not only fixed cost but also variable cost, and they found it be a mixed 0-1 linear program, and it does not have polynomial time algorithm.
By the method of reproducing kernel and the tensor product of operator, the explicit representation of the best Hermite interpolation operator ( H U 2m, 2n u )( x, y ) for the bivariate functions is given, which is not in polynomial form.
In 1947, Danzig presented the conception of linear programming and the famous simplex algorithm. Although the simplex method is efficient in practical application, it is not the polynomial time algorithm and has the lower calculation efficiency in theory.
That is to say, we can not use any polynomial algorithm to solve this kind of problems.
A posteriori error estimate based on extrapolation for p extension is presented using the sequence transformation technique. When the exact solution is smooth, the error in energy norm can be estimated by ε algorithm while when not smooth, polynomial extrapolation is used.

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