polyval: Evaluating a Polynomial

In pracma: Practical Numerical Math Functions

Description

Evaluate polynomial on vector or matrix.

Usage

  polyval(p, x)

  polyvalm(p, A)

Arguments

p	vector representing a polynomial.
x	vector of values where to evaluate the polynomial.
A	matrix; needs to be square.

Details

polyval valuates the polynomial given by p at the values specified by the elements of x. If x is a matrix, the polynomial will be evaluated at each element and a matrix returned.

polyvalm 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 matrix A must be a square matrix.

Value

Vector of values, resp. a matrix.

See Also

poly, roots

Examples

  # Evaluate 3 x^2 + 2 x + 1 at x = 5, 7, and 9
  p = c(3, 2, 1);
  polyval(p, c(5, 7, 9))    # 86  162  262

  # Apply the characteristic polynomial to its matrix
  A <- pascal(4)
  p <- pracma::Poly(A)      # characteristic polynomial of A
  polyvalm(p, A)            # almost zero 4x4-matrix

Example output

[1]  86 162 262
             [,1]         [,2]         [,3]         [,4]
[1,] 2.715272e-12 9.574563e-12 2.215472e-11 4.222400e-11
[2,] 9.695356e-12 3.281742e-11 7.533174e-11 1.424922e-10
[3,] 2.220801e-11 7.457501e-11 1.699593e-10 3.207958e-10
[4,] 4.180478e-11 1.393836e-10 3.171046e-10 5.975781e-10

pracma documentation built on Dec. 11, 2021, 9:57 a.m.