labels SciMax Toolbox laguerre

SciMax Toolbox >> lagrange

lagrange

Maxima Function

Calling Sequence

lagrange (points)
lagrange(points,option)

Description

Computes the polynomial interpolation by the Lagrangian method. Argument points must be either:

In the first two cases the pairs are ordered with respect to the first coordinate before making computations.

With the option argument it is possible to select the name for the independent variable, which is 'x by default; to define another one, write something like varname='z.

Note that when working with high degree polynomials, floating point evaluations are inestable.

Examples:

(%i1) load(interpol)$
(%i2) p:[[7,2],[8,2],[1,5],[3,2],[6,7]]$
(%i3) lagrange(p);
                 4        3         2
             73 x    701 x    8957 x    5288 x   186
(%o3)        ----- - ------ + ------- - ------ + ---
              420     210       420      105      5
(%i4) f(x):=''%;
                     4        3         2
                 73 x    701 x    8957 x    5288 x   186
(%o4)    f(x) := ----- - ------ + ------- - ------ + ---
                  420     210       420      105      5
(%i5) /* Evaluate the polynomial at some points */
      map(f,[2.3,5/7,%pi]);
                             919062
(%o5)  [- 1.567534999999992, ------,
                             84035
                         4          3           2
                   73 %pi    701 %pi    8957 %pi    5288 %pi   186
                   ------- - -------- + --------- - -------- + ---]
                     420       210         420        105       5
(%i6) %,numer;
(%o6) [- 1.567534999999992, 10.9366573451538, 2.89319655125692]
(%i7) load(draw)$  /* load draw package */
(%i8) /* Plot the polynomial together with points */
      draw2d(
        color      = red,
        key        = "Lagrange polynomial",
        explicit(f(x),x,0,10),
        point_size = 3,
        color      = blue,
        key        = "Sample points",
        points(p))$
(%i9) /* Change variable name */
      lagrange(p, varname=w);
                 4        3         2
             73 w    701 w    8957 w    5288 w   186
(%o9)        ----- - ------ + ------- - ------ + ---
              420     210       420      105      5
labels SciMax Toolbox laguerre