Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10333938 | Theoretical Computer Science | 2011 | 13 Pages |
Abstract
We give a high precision polynomial-time approximation scheme for the supremum of any honest n-variate (n+2)-nomial with a constant term, allowing real exponents as well as real coefficients. Our complexity bounds count field operations and inequality checks, and are quadratic in n and the logarithm of a certain condition number. For the special case of n-variate (n+2)-nomials with integer exponents, the log of our condition number is sub-quadratic in the sparse size. The best previous complexity bounds were exponential in the sparse size, even for n fixed. Along the way, we partially extend the theory of Viro diagrams and A-discriminants to real exponents. We also show that, for any fixed δ>0, deciding whether the supremum of an n-variate (n+nδ)-nomial exceeds a given number is NPR-complete.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Philippe Pébay, J. Maurice Rojas, David C. Thompson,