Polynomials, MATLAB in Statistics

Polynomials:

Simple curves are polynomials of various degrees, or orders. The degree is the integer of the highest exponent in the expression. The illustrations are as follows:

  • A straight line is the first order or degree 1 polynomial of the form ax + b, or more clearly ax1+ b.
  • A quadratic is a second order (or degree 2) polynomial of the form ax2 + bx + c.
  • A cubic (degree 3) is of the form ax3 + bx2 + cx + d.

A MATLAB represents a polynomial as a row vector of coefficients. For illustration, the polynomial x3 + 2x2 - 4x + 3 would be represented by the vector [1 2 -4 3].

The polynomial 2x4 - x2 + 5 would be represented by [2 0 -1 0 5]; note that the zero terms for x3 and x1.

There are built-in functions sym2poly and poly2sym which convert symbolic expressions to polynomial vectors and vice versa, the illustration is as shown below:

>> myp = [1,2,-4,3];

>> poly2sym(myp)

ans =

x^3+2*x^2-4*x+3

>> mypoly = [2 0 -1 0 5];

>> poly2sym(mypoly)

ans =

2*x^4-x^2+5

>> sym2poly(ans)

ans =

2 0 -1 0 5

Posted Date: 10/22/2012 8:40:45 AM | Location : United States







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