Interpolation and Approximation
Interpolation and Approximation
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DOI：
10.1007/978-1-84996-095-3_18
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
P. Revesz
中科院分区：
文献类型：
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作者：
P. Revesz
大多数工程和科学现象，例如地貌表面或某个位置不断变化的温度，本质上在空间或时间或两者上都是无限的。我们无法测量所有数据。通常，可以只记录某些特定位置和时间的表面高程值或温度。但是，可以根据测量的位置和时间来估计未测量的位置和时间的值。该估计可以通过插值或近似来完成。插值和近似方法都为整个研究现象开发了一些插值函数，例如对于温度来说是温度函数，对于景观高程来说是表面函数。插值函数保留测量值，而近似函数更通用，它们可能不保留各个测量值。插值函数和逼近函数通常用约束来表示，因此它们可以方便地在约束数据库中表示。18.1节描述了线性插值，它经常用于估计部分已知函数的缺失值。
Most engineering and scientific phenomena, such as the surface of a landscape or the continuously changing temperature at a location are inherently infinite in space or time or both. We cannot measure all the data. Generally it is possible to record surface elevation values or the temperature only at some specific locations and times.However, it is possible to estimate the values at the unmeasured locations and times from the measured ones. This estimation can be done byinterpolationorapproximation. Both interpolation and approximation methods develop for the entire studied phenomena some interpolation functions, such as for temperature a temperature function and for the landscape elevation a surface function. Interpolation functions preserve the measured values, while approximation functions are more general, and they may not preserve the individual measured values. The interpolation and approximation functions are usually expressed by constraints, hence they can be conveniently represented in constraint databases.Section 18.1 describeslinear interpolation, which is used frequently to estimate the missing values of a partially known function.