### Basic Examples

Basic Examples

A rational interpolation of degree (2,4) to at seven equally spaced points between 0 and 2:

[E^x,{x,2,4},Range[0,2,1/3]]

In[]:=

1.+0.379962x+0.0469528x

2

1-0.620029x+0.166914x-0.0234058x+0.00145279x

2

3

4

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The error between the function and the approximation tends to get larger near the endpoints:

Plot[%-E^x,{x,0,2},PlotRangeAll]

In[]:=

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Automatically chosen the interpolation points: result in a smaller maximum error:

[E^x,{x,2,4},{x,0,2}]

In[]:=

1.+0.379827x+0.0468693x/1-0.620166x+0.166978x-0.0234119x+0.00145192x

2

2

3

4

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Plot[%-E^x,{x,0,2}]

In[]:=

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### Options

Options

#### “Bias”

“Bias”

Bias the distribution of the points to the right to get smaller errors there and larger errors to the left:

[E^x,{x,2,4},{x,0,2},"Bias".25]

In[]:=

1.+0.386186x+0.0491526x

2

1-0.613792x+0.16282x-0.0223404x+0.0013436x

2

3

4

Out[]=

Plot[%-E^x,{x,0,2}]

In[]:=

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