کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4649982 1342471 2008 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Estimates of the Pythagoras number of Rm[x1,…,xn]Rm[x1,…,xn] through lattice points and polytopes
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Estimates of the Pythagoras number of Rm[x1,…,xn]Rm[x1,…,xn] through lattice points and polytopes
چکیده انگلیسی

Hilbert’s 17th Problem launched a number of inquiries into sum-of-squares representations of polynomials over the real numbers. Choi, Lam, and Reznick gave some bounds on the number of squares required for such a representation and indicated some directions for improving these bounds. In the first part of this paper, we follow their suggestion and obtain some stronger bounds. In the second part, we show that in the case of homogeneous polynomials in three variables, this technique cannot be extended further.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 308, Issue 23, 6 December 2008, Pages 5771–5781
نویسندگان
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