Info Catalog octave: Polynomial Manipulations octave: Finding Roots

octave: Evaluating Polynomials

 
 28.1 Evaluating Polynomials
 ===========================
 
 The value of a polynomial represented by the vector C can be evaluated
 at the point X very easily, as the following example shows:
 
      N = length (c) - 1;
      val = dot (x.^(N:-1:0), c);
 
 While the above example shows how easy it is to compute the value of a
 polynomial, it isn’t the most stable algorithm.  With larger polynomials
 you should use more elegant algorithms, such as Horner’s Method, which
 is exactly what the Octave function ‘polyval’ does.
 
    In the case where X is a square matrix, the polynomial given by C is
 still well-defined.  As when X is a scalar the obvious implementation is
 easily expressed in Octave, but also in this case more elegant
 algorithms perform better.  The ‘polyvalm’ function provides such an
 algorithm.
 
  -- : Y = polyval (P, X)
  -- : Y = polyval (P, X, [], MU)
  -- : [Y, DY] = polyval (P, X, S)
  -- : [Y, DY] = polyval (P, X, S, MU)
 
      Evaluate the polynomial P at the specified values of X.
 
      If X is a vector or matrix, the polynomial is evaluated for each of
      the elements of X.
 
      When MU is present, evaluate the polynomial for (X-MU(1))/MU(2).
 
      In addition to evaluating the polynomial, the second output
      represents the prediction interval, Y +/- DY, which contains at
      least 50% of the future predictions.  To calculate the prediction
      interval, the structured variable S, originating from ‘polyfit’,
      must be supplied.
 
DONTPRINTYET       See also: polyvalm XREFpolyvalm, *notepolyaffine:
DONTPRINTYET       See also: polyvalm XREFpolyvalm, polyaffine

      XREFpolyaffine, polyfit XREFpolyfit, roots XREFroots,
      poly XREFpoly.
 
  -- : polyvalm (C, X)
      Evaluate a polynomial in the matrix sense.
 
      ‘polyvalm (C, X)’ will evaluate the polynomial in the matrix sense,
      i.e., matrix multiplication is used instead of element by element
      multiplication as used in ‘polyval’.
 
      The argument X must be a square matrix.
 
DONTPRINTYET       See also: polyval XREFpolyval, roots XREFroots, *noteDONTPRINTYET       See also: polyval XREFpolyval, roots XREFroots, 
      poly XREFpoly.
 

Info Catalog octave: Polynomial Manipulations octave: Finding Roots