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## 27.1 Evaluating Polynomials

The value of a polynomial represented by the vector `c` can be evaluated
at the point `x` very easily, as the following example shows:

N = length(c)-1; val = dot( x.^(N:-1:0), c ); |

While the above example shows how easy it is to compute the value of a
polynomial, it isn't the most stable algorithm. With larger polynomials
you should use more elegant algorithms, such as Horner's Method, which
is exactly what the Octave function `polyval`

does.

In the case where `x` is a square matrix, the polynomial given by
`c` is still well-defined. As when `x` is a scalar the obvious
implementation is easily expressed in Octave, but also in this case
more elegant algorithms perform better. The `polyvalm`

function
provides such an algorithm.

__Function File:__`y`=**polyval***(*`p`,`x`)__Function File:__`y`=**polyval***(*`p`,`x`, [],`mu`)Evaluate the polynomial at of the specified values for

`x`. When`mu`is present evaluate the polynomial for (`x`-`mu`(1))/`mu`(2). If`x`is a vector or matrix, the polynomial is evaluated for each of the elements of`x`.__Function File:__[`y`,`dy`] =**polyval***(*`p`,`x`,`s`)__Function File:__[`y`,`dy`] =**polyval***(*`p`,`x`,`s`,`mu`)In addition to evaluating the polynomial, the second output represents the prediction interval,

`y`+/-`dy`, which contains at least 50% of the future predictions. To calculate the prediction interval, the structured variable`s`, originating form `polyfit', must be present.**See also:**polyfit, polyvalm, poly, roots, conv, deconv, residue, filter, polyderiv, polyinteg.

__Function File:__**polyvalm***(*`c`,`x`)Evaluate a polynomial in the matrix sense.

`polyvalm (`

will evaluate the polynomial in the matrix sense, i.e., matrix multiplication is used instead of element by element multiplication as is used in polyval.`c`,`x`)The argument

`x`must be a square matrix.**See also:**polyval, poly, roots, conv, deconv, residue, filter, polyderiv, polyinteg.

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