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Unformatted text preview: you want to plot your data as discrete points.
For example, the command
>> plot(x,y,’ro’) The
Polynomial % or try plot(x,y,’g*’) will produce an image similar to that shown in Figure 2. 4
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−1 0 1 2 3 4 5 Figure 2 Using markers to display discrete data points. Plotting Polynomials in Matlab
If Matlab’s plot command connects consecutive points with line segments, it seems at ﬁrst
hopeless that one can plot smooth, continuous curves. However, one can provide a fair approx- back
exit imation of the graph of a curve by sampling the curve at a lot of points. If enough points are
used, the curve drawn with the plot command will take on a smooth appearance.
To produce the smooth shape of a polynomial in Matlab, you ﬁrst have to generate a suﬃcient
number of data points that satisfy the equation of the polynomial. The following commands
produce the graph of the polynomial p(x) = x 3 − 6x 2 + 3x + 10 over the interval [−2, 6], as
shown in Figure 3.
>> p=[1 -6 3 10];
Polynomial %You need a lot of points to draw a smooth curve. Matlab’s linspace command is an easy way to generate a vector of equally spaced points. By
default, the command linspace(a,b) generates 100 equally spaced points, starting at a and
ending at b. You can generate more points with the syntax is linspace(a,b,N). For example,
the command linspace(0,1,1000) generates 1000 equally spaced points, starting at 0 and
ending at 1000. title page
previous page The Interpolating Polynomial
Given a set of data points, scientists and mathematicians often need to ﬁnd a polynomial of
speciﬁed degree whose graph passes through each of the given data points. Such a polynomial
is called an interpolating polynomial. 3
In this exercise, we will ﬁnd a third degree polynomial that passes through the points (−3, 0),
(−2, −3), (0, 3), and (2, −15). A third degree polynomial has th...
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This document was uploaded on 02/14/2014.
- Summer '12