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Results tagged with polynomials
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user 9652
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
6
votes
1
answer
491
views
Polynomials with prescribed points to match prescribed bounds
Background: I know that the fact about nonnegative polynomials
with presribed zeros can be generalized to "generalized
polynomials" built from Tchebycheff-systems (due to a theorem by
Krein). … I would love to see a similar theorem on bounded
generalized polynomials which attain the bounds at prescribed points. …
- 12.7k
11
votes
Why do roots of polynomials tend to have absolute value close to 1?
I offer another point of view from the angle of the companion matrix of the polynomial. It may also give a very vague intuition about the observed uniformity of the distribution along the unit circle. …
- 12.7k
3
votes
Why are the angular differences of these random complex polynomial coefficients almost const...
I suspect both numerical issues and issues with the random number generator to be at work simulaneously.
I also get crazy values (i.e. very large ones and also some structure as shown above) for the …
- 12.7k
0
votes
Approximating a function with sums of powers
You may want to restrict $x$ to be positive and then expressions of the type you are dealing with called "posynomials" if the $c_k$ are also positive. Posynomials are convex and they are indeed used i …
- 12.7k
10
votes
What function is this? -Counterexample found: it is not Lipschitz-
I don't know if this is what you are looking for, but the (essential) supremum of a function can be written as an integral with respect to a (non-additive) measure (namely, the sign of the Lebesgue-me …
- 12.7k
4
votes
Roots of modified polynomials
I guess, Chapter 2, §1 of "Perturbation Theory of Linear Operators" by Kato will answer your question.
- 12.7k