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Unformatted text preview: + 0x 3 + 0x 2 − 4x − 3, or, more simply, q(x) = 2x 4 − 4x − 3.
Note that your must use zeros to denote the missing terms of the polynomial. previous page Some polynomials and their Matlab representations are displayed in Table 1. Note well the
use of zeros as placeholders. contents next page
print doc Evaluating a Polynomial in Matlab
Matlab has a number of useful routines for working with polynomials. 1 . One particularly useful
1 Use Matlab’s help facility to examine the help ﬁles for roots and poly. Although these routines will not be used in this close
exit p (x) = x 3 − x 2 − 1 p=[1 -1 0 -1]
q(x) = x 4 − x 2 − x q=[1 0 -1 -1 0]
r (x) = x 4 − 2x 2 r=[1 0 -2 0 0] The
Polynomial Table 1 Matlab represents polynomials with vectors.
routine is polyval. Enter the following command at the Matlab prompt to generate the resulting
>> help polyval
POLYVAL Polynomial evaluation.
Y = POLYVAL(P,X), when P is a vector of length N+1 whose elements
are the coefficients of a polynomial, is the value of the
polynomial evaluated at X. title page
contents Y = P(1)*XˆN + P(2)*Xˆ(N-1) + ... + P(N)*X + P(N+1) previous page
If X is a matrix or vector, the polynomial is evaluated at all
points in X. See also POLYVALM for evaluation in a matrix sense.
If p is a polynomial and x is a number, then polyval(p,x) evaluates the polynomial at the
number x. For example, if p(x) = x 3 + 2x − 8, then p(−2) = −20.
>> p=[1 0 2 -8];
>> y=polyval(p,x) activity, you will have occasion to use them in later activities. next page
-20 The Matlab can evaluate a polynomial at each element of a vector or matrix. 2 For example, use your
calculator to verify these calculations: p(x) = x 3 + 2x − 8, then p(−2) = −20, p(−1) = −11,
p(0) = −8, p(1) = −5, and p(2) = 4. It is not diﬃcult to evaluate the polynomial at each x -value;
it’s just tedious. Matlab saves you some eﬀort by evaluating the polynomial at each value of x
with one command....
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This document was uploaded on 02/14/2014.
- Summer '12