英语翻译The approximation (5) leads to the following bounds onth

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英语翻译
The approximation (5) leads to the following bounds on
the average weighted squared error:
This upper bound is tight because it would be achieved for
a spectrum Fm that is concentrated entirely on the worstcase
frequency.In light of this tight bound,it is desirable
to design the scaling factors s and the interpolation coefficients
u(x) to minimize the worst-case error by the following
min–max criterion (cf.[4,Eq.(10)]):
Finding u(x) by minimizing (15) is simply a weighted
least-squares problem that is linear in u.Solving that minimization
directly leads to complex expressions,e.g.[1,Eq.
(7)] that perhaps shroud the nature of the interpolator.For
more insight,we rewrite the error as follows (cf.[4,Eq.
(14)]):

（5）式的近似导致了以下对加权平均平方误差的范围：这个上限是严密的,因为它将实现一个光谱调频,这是完全基于最坏情况下的频率.鉴于这种严密的范围,人们希望设计的缩放因子和插值系数u（x）通过以下最小-最大准则–最小化误差（参见[ 4,方程（10）]）得到：通过最小化（15）式找到U（x）,这是一个简单的加权最小二乘问题,在u（x）中这个问题是线性的.最小化直接导致复杂的表达式,例如[ 1,方程（7）],也许覆盖了内插的性质.为了更深入地了解,我们改写误差如下（参见[ 4,方程（14）]）：

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