## Kodai Mathematical Journal

- Kodai Math. J.
- Volume 39, Number 2 (2016), 253-275.

### Sufficient conditions for a real polynomial to be a sum of squares of polynomials

Van Doat Dang and Thi Thao Nguyen

#### Abstract

In this paper, we establish new sufficient conditions for the polynomial *f* to be SOS in terms of the Newton polyhedron of *f* (Theorems 2.6 and 2.12). These new sufficient conditions include results which were proved earlier by Lasserre [13, Theorem 3], Fidalgo and Kovacec [6, Theorem 4.3], Ghasemi and Marshall [7, Theorems 2.1 and 2.3], and Ghasemi and Marshall [8, Theorem 2.3].

#### Article information

**Source**

Kodai Math. J., Volume 39, Number 2 (2016), 253-275.

**Dates**

First available in Project Euclid: 6 July 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.kmj/1467830136

**Digital Object Identifier**

doi:10.2996/kmj/1467830136

**Mathematical Reviews number (MathSciNet)**

MR3520511

**Zentralblatt MATH identifier**

06624561

#### Citation

Dang, Van Doat; Nguyen, Thi Thao. Sufficient conditions for a real polynomial to be a sum of squares of polynomials. Kodai Math. J. 39 (2016), no. 2, 253--275. doi:10.2996/kmj/1467830136. https://projecteuclid.org/euclid.kmj/1467830136