Titlebook: Complexity Theory of Real Functions; Ker-I Ko Book 1991 Birkhäuser Boston 1991 Approximation.NP-completeness.Notation.algorithm.algorithms

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单片眼镜

Differentiation,rd to compute from the approximation of the function. However, if some nice properties about the function is known (such as the differentiability of the derivative itself) then the derivative may be easy to compute. Formally, we prove that the derivative of a polynomial-time computable function is p

鞭打

Ordinary Differentiation Equations,by a polynomial-time computable function . on the rectangle [0,1] × [-1,1]. We consider only ordinary differential equations of the first order, and only equations with initial conditions. The complexity of the solutions . of equation (7.1) depends on certain properties of the function .. First, if

DEMN

Approximation by Polynomials,mial function . such that .(.(. 2. for all . ∈ [0, 1], In this chapter we investigate the polynomial-time version of the Weierstrass approximation theorem: Is the sequence |.} polynomial-time computable, if . is known to be polynomial-time computable? Pour-El and Caldwell [1975] proved that the recu

PANG

An Optimization Problem in Control Theory,es the Lipschitz condition, compute the minimum value . Intuitively, the function . may be viewed as the cost function on inputs ., . ∈ [0, 1] and the corresponding decisions .(.) and .(.) on these inputs. The decision functions . and . are based only on part of the input values and perform, in a se

thalamus

Daily-Value

Model Complexity Control in Clusteringtion . on [0,1]. It is to be shown that these maximum values axe exactly the real numbers which have a (general) left cut in . (called left . real numbers). For two-dimensional, polynomial-time computable functions . on [0, l]., the maximum functions .) = max{., .)| 0 ≤ . ≤ 1} coincide with . real f

Ligneous

https://doi.org/10.1007/978-3-319-59072-1e restrict our attention to the class of continuous functions which have polynomial moduli of continuity, then it is not known whether the notion of polynomial-time approximability is strictly stronger than the notion of polynomial-time computability.

歪曲道理

无关紧要

Biao Luo,Derong Liu,Xiong Yang,Hongwen Maeierstrass approximation theorem does hold and so a polynomial-time evaluable straight-line program for . can be found in polynomial time if . is itself polynomial-time computable. However, the strong form of the theorem that requires the output of the coefficients of . fails. Thus, the integrals of