7/18/2019 Piecewise Cubic Hermite Interpolating Polynomial

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Piecewise Cubic Hermite Interpolating Polynomial (PCHIP)

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Syntaxyi = pchip(x,y,xi)

pp = pchip(x,y)

Description

yi = pchip(x,y,xi) returns vector yi containing elements corresponding to the elements of xi

and determined by piecewise cubic interpolation within vectors x and y. The vector x specifies

the points at which the data y is given. If y is a matrix then the interpolation is performed for

each column of y and yi is length(xi)!by!size(y,2).

pp = pchip(x,y) returns a piecewise polynomial structure for use by ppval. x can be a row or

column vector. y is a row or column vector of the same length as x or a matrix with length(x) 

columns.

pchip finds values of an underlying interpolating function at intermediate points such that"

• #n each subinterval is the cubic Hermite interpolant to the given

values and certain slopes at the two endpoints.

• interpolates  y i.e. and the first derivative is continuous. is

 probably not continuous$ there may be %umps at the .

• The slopes at the are chosen in such a way that preserves the shape of the data

and respects monotonicity. This means that on intervals where the data are monotonic so

is $ at points where the data has a local extremum so does .

Note  If  y is a matrix satisfies the above for each column of  y.

Examples

x = -3:3;

y = [-1 -1 -1 0 1 1 1];

t = -3:.01:3;

7/18/2019 Piecewise Cubic Hermite Interpolating Polynomial

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p = pchip(x,y,t);

s = spline(x,y,t);

plot(x,y,o,t,p,-,t,s,-.)

legen!(!ata,pchip,spline,")