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Results tagged with polynomials
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user 5963
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.
5
votes
Accepted
Positive polynomials
There are algorithmic techniques such as sums-of-squares and semidefinite programming which can in practice certify positivity of many polynomials (globally, or as you want here, on sets such as the positive …
- 8,501
2
votes
Accepted
Approximation by polynom 1) with respect to supremum-norm 2) I need F_{approx} > F_{exact}
The simplest are the sums of squares: a polynomial which is a sum of squares of other polynomials (hereafter a "sum of squares") is always nonnegative. … Similar ideas work for constraints that polynomials be nonnegative on intervals, boxes, etc. …
- 8,501
2
votes
Solving a System of Quadratic Equations
What you have is an instance of a quadratically constrained quadratic program (QCQP). These problems are NP-hard in general (though it's possible your particular type of instance is not hard as fedja …
- 8,501
14
votes
Accepted
Effective algorithm to test positivity
In particular one can check sufficient conditions like whether $f$ is a sum of squares of polynomials (and a hierarchy of tighter conditions) in polynomial time using semidefinite programming, and often …
- 8,501