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Results tagged with polynomials
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user 82122
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.
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approximation of rational functions
Suppose $\hat{p}/\hat{q}$ and $p/q$ are two rational functions where $p,q,\hat{p},\hat{q}$ are of degree $n$. Suppose they satisfy that $|p(z)/q(z) - \hat{p}(z)/\hat{q}(z)| < \epsilon$ for any $z$ on …
- 181
0
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1
answer
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approximation of products of polynomials
I am wondering whether the following can be proved:
Suppose $p(z)$ and $q(z)$ are polynomials of degree $n$ with real coefficients and leading coefficient 1. … Suppose there are other two degree $n$ polynomials $\hat{p}$ and $\hat{q}$ with leading coefficients 1 such that for any $z$ on unit circle,
$$ |p(z)\hat{q}(z) - q(z)\hat{p}(z)| \le \epsilon.$$
There …
- 181