Optimization and NP_R-Completeness of Certain Fewnomials Conference Paper

abstract

• optimizing, sparse, BSS model, real, exponential sum, polynomial-time, circuit, approximate, condition number 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 polynomial in n and the logarithm of a certain condition number. For the special case of polynomials (i.e., 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 A-discriminants to real exponents and exponential sums, and find new and natural NPR-complete problems. Copyright 2009 ACM.

name of conference

• Proceedings of the 2009 conference on Symbolic numeric computation

authors

• Rojas, Joseph

published proceedings

• SNC'09: PROCEEDINGS OF THE 2009 INTERNATIONAL WORKSHOP ON SYMBOLIC-NUMERIC COMPUTATION

author list (cited authors)

• Pebay, P., Rojas, J. M., & Thompson, D. C.

citation count

• 4

complete list of authors

• Pebay, Philippe||Rojas, J Maurice||Thompson, David C

publication date

• August 2009

publisher

• Association for Computing Machinery (ACM)  Publisher

keywords

• Approximate
• Bss Model
• Circuit
• Condition Number
• Exponential Sum
• Optimizing
• Polynomial-time
• Real
• Sparse

Digital Object Identifier (DOI)

• 10.1145/1577190.1577212

International Standard Book Number (ISBN) 13

• 978-1-60558-664-9

start page

• 133

end page

• 141

URL

• http://dx.doi.org/10.1145/1577190.1577212