constructs an interpolating polynomial in x which reproduces the function values f_(i) at successive integer values 1, 2, of x.

constructs an interpolating polynomial for the function values f_(i) corresponding to x values x_(i).

constructs a multidimensional interpolating polynomial in the variables x, y, .

constructs an interpolating polynomial that reproduces derivatives as well as function values.

Details and OptionsDetails and Options

  • The function values f_(i) and sample points x_(i), 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 n^(th) 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 n. »

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Construct an interpolating polynomial for the squares:

Click for copyable input

Check the result:

Click for copyable input

Construct an interpolating polynomial through three points:

Click for copyable input

Check the result at a single point:

Click for copyable input
Introduced in 1991
| Updated in 2007