BUILT-IN MATHEMATICA SYMBOL

# InterpolatingPolynomial

InterpolatingPolynomial[{f1, f2, ...}, x]
constructs an interpolating polynomial in x which reproduces the function values at successive integer values 1, 2, ... of .

InterpolatingPolynomial[{{x1, f1}, {x2, f2}, ...}, x]
constructs an interpolating polynomial for the function values corresponding to values .

InterpolatingPolynomial[{{{x1, y1, ...}, f1}, {{x2, y2, ...}, f2}, ...}, {x, y, ...}]
constructs a multidimensional interpolating polynomial in the variables x, y, ....

InterpolatingPolynomial[{{{x1, ...}, f1, df1, ...}, ...}, {x, ...}]
constructs an interpolating polynomial that reproduces derivatives as well as function values.

## Details and OptionsDetails and Options

• The function values and sample points , etc. can be arbitrary real or complex numbers, and in 1D can be arbitrary symbolic expressions.
• With a 1D list of data of length , InterpolatingPolynomial gives a polynomial of degree .
• With any given specified set of data, there are infinitely many possible interpolating polynomials; InterpolatingPolynomial always tries to find the one with lowest total degree.
• InterpolatingPolynomial gives the interpolating polynomial in a Horner form, suitable for numerical evaluation.
• Different elements in the data can have different numbers of derivatives specified.
• For multidimensional data, the derivative can be given as a tensor with a structure corresponding to D[f, {{x, y, ...}, n}]. »
• InterpolatingPolynomial allows any function value or derivative to be given as Automatic, in which case it will attempt to fill in the necessary information from derivatives or other function values. »
• The option setting Modulus->n specifies that the interpolating polynomial should be found modulo . »

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Construct an interpolating polynomial for the squares:

 Out[1]=

Check the result:

 Out[2]=

Construct an interpolating polynomial through three points:

 Out[1]=

Check the result at a single point:

 Out[2]=

## TutorialsTutorials

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