mean value of polynominal function

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Christoph Thorwartl 2020-7-24

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评论： Christoph Thorwartl 2020-7-24

采纳的回答： KSSV

Given is a polynomial function k. I would like to calculate the mean value of the function between two points (x1, x2).

This solution is too imprecise for my purpose.

mean = (polyval(k,x2) + polyvalk,x1))/2

I would be very grateful for any feedback.

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KSSV 2020-7-24

Don't use the variable name as mean. It is an inbuilt function.

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Answer 1

KSSV 2020-7-24

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m = 1000 ; 
x = linspace(x1,x2,m) ; 
y = polyval(k,x) ; 
iwant = mean(y) ; 

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Christoph Thorwartl 2020-7-24

Thank you!

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Answer 2

John D'Errico 2020-7-24

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编辑：John D'Errico 2020-7-24

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The average value of a function over some interval is just the definite integral of the function, then divided by the length of the interval. Goes back to basic calc.

Since you are talking about using polyval, then I assume the polynomial is in the form of coefficients, appropriate for polyval. As an example, consider the quadratic polynomial x^2 - x + 2, on the interval [1,3].

k = [1 -1 2];
x12 = [1 3];
format long g
>> diff(polyval(polyint(k),x12))/diff(x12)
ans =
          4.33333333333333

If you want to verify the result:

syms x
K = x^2 - x + 2;
int(K,x12)/diff(x12)
ans =
13/3

They agree, as they should.

In both cases, this yields the exact result for that polynomial, not an approximation. Exact at least to within the limits of floating point arithmetic.

If you want a reference, this should do:

https://en.wikipedia.org/wiki/Mean_of_a_function