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Home : Support : Online Help : Mathematics : Numerical Computations : Interpolation and Curve Fitting : CurveFitting Package : CurveFitting/PolynomialInterpolation

CurveFitting

  

PolynomialInterpolation

  

compute an interpolating polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

PolynomialInterpolation(xydata, v, opts)

PolynomialInterpolation(xdata, ydata, v, opts)

Parameters

xydata

-

list, Array, or Matrix of the form [[x1,y1], [x2,y2], ..., [xn,yn]]; data points

v

-

name or numeric value

opts

-

(optional) equation of the form form=option where option is one of Lagrange, monomial, Newton, or power; specify keyword describing form of output

xdata

-

list, Array, or Vector of the form [x1, x2, ..., xn]; independent values

ydata

-

list, Array, or Vector of the form [y1, y2, ..., yn]; dependent values

Description

• 

The PolynomialInterpolation routine returns the polynomial of degree less than or equal to n1 in variable v that interpolates the points {x1,y1,x2,y2,...,xn,yn}.  If v is a numerical value, the value of the polynomial at this point is returned.

• 

You can call the PolynomialInterpolation routine in two ways.

  

The first, PolynomialInterpolation(xydata, v, opts), accepts a list, Array, or Matrix, [[x1,y1],[x2,y2],...,[xn,yn]], of data points.

  

The second, PolynomialInterpolation(xdata, ydata, v, opts), accepts two lists, two Arrays, or two Vectors. In this form, the first set of data contains the independent values, [x1,x2,...,xn], and the second set contains the dependent values, [y1,y2,...,yn].  Each element must be of type algebraic and all of the independent values must be distinct.

Examples

withCurveFitting:

PolynomialInterpolation0,0,1,3,2,1,3,3,z

32z37z2+172z

(1)

PolynomialInterpolation0,2,4,7,2,a,1,3,3

1970+35a

(2)

PolynomialInterpolation0,2,4,7,2,a,1,3,z,form=Lagrange

128z2z4z7+120azz4z7124zz2z7+135zz2z4

(3)

See Also

CurveFitting

type/algebraic

 


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