# polyval

Polynomial evaluation

## Syntax

y = polyval(p,x)
[y,delta] = polyval(p,x,S)
y = polyval(p,x,[],mu)
[y,delta] = polyval(p,x,S,mu)

## Description

y = polyval(p,x) returns the value of a polynomial of degree n evaluated at x. The input argument p is a vector of length n+1 whose elements are the coefficients in descending powers of the polynomial to be evaluated.

y = p1xn + p2xn–1 + … + pnx + pn+1

x can be a matrix or a vector. In either case, polyval evaluates p at each element of x.

[y,delta] = polyval(p,x,S) uses the optional output structure S generated by polyfit to generate error estimates delta. delta is an estimate of the standard deviation of the error in predicting a future observation at x by p(x). If the coefficients in p are least squares estimates computed by polyfit, and the errors in the data input to polyfit are independent, normal, and have constant variance, then y±delta contains at least 50% of the predictions of future observations at x.

y = polyval(p,x,[],mu) or [y,delta] = polyval(p,x,S,mu) use $\stackrel{^}{x}=\left(x-{\mu }_{1}\right)/{\mu }_{2}$ in place of x. In this equation, ${\mu }_{1}=\text{mean}\left(x\right)$ and ${\mu }_{2}=\text{std}\left(x\right)$. The centering and scaling parameters mu = [μ1,μ2] are optional output computed by polyfit.

## Examples

The polynomial $p\left(x\right)=3{x}^{2}+2x+1$ is evaluated at x = 5, 7, and 9 with

p = [3 2 1];
polyval(p,[5 7 9])

which results in

ans =

86   162   262

For another example, see polyfit.

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### Tips

The polyvalm(p,x) function, with x a matrix, evaluates the polynomial in a matrix sense. See polyvalm for more information.