Smoothers

Smoothers - EXAMPLES OF SMOOTHERS FOR SPATIAL INTERPOLATION...

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EXAMPLES OF SMOOTHERS FOR SPATIAL INTERPOLATION IN GEOSTATISTICAL ANALYST ESE 502 Tony E. Smith
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Local Polynomial Fit Radial Basis Fit Spline Function Fit Ordinary Krige Fit
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LOCAL LINEAR POLYNOMIAL FIT
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RADIAL BASIS FUNCTIONS Given data ( , ) , 1,. ., ii sy i n = , Choose normal densities: 2 , 1 2 () ( ) , ., 2 exp i i ss si n π φ ⎛⎞ == ⎜⎟ ⎝⎠ Let ( :1 ., ), [ ( ) : , ., ] j yy n s i j n Φ = = , and Find coefficients ( : ., ) i aa i n = = such that y a = Φ 1 a y ⇒= Φ
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-2 0 2 4 6 8 10 12 14 16 18 20 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 RBF with Inverse Quadratic Basis Functions
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0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 RADIAL BASIS INTERPOLATION ( Normal Density Family )
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CUBIC SPLINE MODELS For simplicity we focus on the one-dimensional case, and consider a set of data points {( , ) : 1,. ., } ii x yi n = , such as the 5 n = points in Figure 1 below: The objective is to find a smooth curve, () yc x = , that passes through these data points, such as the curve shown in Figure 2. 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 1. Data Points
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Smoothers - EXAMPLES OF SMOOTHERS FOR SPATIAL INTERPOLATION...

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