Polynomial Anonymous function degree

2019 4 27
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更新时间：2019 4 28
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How can I find the degree of a given "anonymous function" like f=@(x) x^2+2x; given the functions are only polynomials?

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dpb
dpb 2019-4-27
编辑：dpb 2019-4-27
Convert to string via func2str and regexp() to return powers of exponentials--find max thereof. Of course, that presumes someone doesn't write a function like using the explicit form of Horner's rule--
f=@(x) (x+2).*x;
in which case you've got more work to do... :)

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Walter Roberson
Walter Roberson 2019-4-27

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Build a vector
X = realmax.^(1./(1:50));
Evaluate the function at X. The first result that is finite is probably the degree. However, it is possible for a polynomial with sufficiently large coefficients to generate an infinity "early", or for with sufficiently small leading coefficient to be "late" relative to this, so you should use that as a starting point to do more cross-checking.

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Ashish Sahu
Ashish Sahu 2019-4-28
Thanks, it seems to work.
Ashish Sahu
Ashish Sahu 2019-4-28
This method doesn't seem to work for degree 4 & degree 5 polynomials.
f=@(x) x^4;
X = realmax.^(1./(1:50));
for i=1:50
Y = f(X(i));
if Y<Inf
break
end
end
degree = i % degree of polynomial is degree
I am getting degree = 5.
Walter Roberson
Walter Roberson 2019-4-28
x^4 is a leading coefficient of 1 which is "suffiently small" in terms of what I wrote above.
Perhaps a slightly different X would help? You should analyze why this case fails to figure out what changes to make.

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