1. Roots of polynomials

  >> f = [ 1 0 -1 0 ]  % f(x) = x**3 - x**2

  >> r = roots(f)
  r= 0
    -1
     1

  >> err = polyval(f,r)   % confirm by evaluation f at the proposed roots

  err = 0
        0
        0

  >> poly(r)          % construct polynomial from roots r

  ans = [ 1 0 -1 0]


2. Roots of functions (non polynomial)

  >> f = @ (x) (sin(x) -x)

  >> r = fzero(f,0);
 
  >> r = fzero('cos(x)-x',0);

  >> err = feval(f,0);

  >> r= fzero(f,[-pi pi]);  % range for roots : bisection

  >> r= fzero(f,[-pi pi], 1e-10);  % tolerance for root finding


  >>  yi = interp1(x,y,xi,method)

  x, y are two given vectors  y(i) = f(x(i)) for all x(i), y(i) i =1 , ... length(x)

  Interpolation determines f such that y=f(x). Then

  yi is going to be computed for given vector xi i.e. yi = f(xi)

  method is one of 'nearest', 'linear', 'spline', 'cubic'