Results 101 to 110 of about 1,163,681 (226)

Isoparametric polynomials and sums of squares

, 2018
The Hilbert's 17th problem asks that whether every nonnegative polynomial can be a sum of squares of rational functions. It has been answered affirmatively by Artin.
Ge, Jianquan, Tang, Zizhou
core  

Sparse Regularization With Reverse Sorted Sum of Squares via an Unrolled Difference-of-Convex Approach

IEEE Open Journal of Signal Processing
This paper proposes a sparse regularization method with a novel sorted regularization function. Sparse regularization is commonly used to solve underdetermined inverse problems.
Takayuki Sasaki, Kazuya Hayase, Masaki Kitahara, Shunsuke Ono   +3 more
doaj   +1 more source

Validation of "sasLM," an R package for linear models with type III sum of squares. [PDF]

Transl Clin Pharmacol, 2020
Sunwoo J, Kim H, Choi D, Bae KS.
europepmc   +1 more source

Perfect powers that are sums of consecutive squares

, 2017
We determine all perfect powers that can be written as the sum of at most 10 consecutive ...
Patel, Vandita
core  

Sum of Cubes is Square of Sum

, 2013
Inspired by the fact that the sum of the cubes of the first $n$ naturals is equal to the square of their sum, we explore, for each $n$, the Diophantine equation representing all non-trivial sets of $n$ integers with this property. We find definite answers to the standard question of infinitude of the solutions as well as several other surprising ...
Barbeau, Edward, Seraj, Samer
openaire   +2 more sources

ON THE COMPLEXITY OF SEMIDEFINITE PROGRAMS ARISING IN POLYNOMIAL OPTIMIZATION

Croatian Operational Research Review, 2012
In this paper we investigate matrix inequalities which hold irrespective of the size of the matrices involved, and explain how the search for such inequalities can be implemented as a semidefinite program (SDP).
Igor Klep, Janez Povh, Angelika Wiegele
doaj  

OPTIMIZATION AND APPROXIMATION OF NC POLYNOMIALS WITH SUMS OF SQUARES

Croatian Operational Research Review, 2010
In this paper we study eigenvalue optimization of non-commutative polynomials. That is, we compute the smallest or biggest eigenvalue a non-commutative polynomial can attain. Our algorithm is based on sums of hermittian squares.
Kristijan Cafuta, Igor Klep
doaj  

Side-constrained minimum sum-of-squares clustering: mathematical programming and random projections

Journal of Global Optimization, 2021
Leo Liberti, Benedetto Manca
semanticscholar   +1 more source

High-Performance Hybrid Algorithm for Minimum Sum-of-Squares Clustering of Infinitely Tall Data

Mathematics
This paper introduces a novel formulation of the clustering problem, namely, the minimum sum-of-squares clustering of infinitely tall data (MSSC-ITD), and presents HPClust, an innovative set of hybrid parallel approaches for its effective solution.
Ravil Mussabayev, Rustam Mussabayev
doaj   +1 more source

Component Analysis When Testing for Fixed Effects in Unbalanced ANOVAs

Stats
In possibly unbalanced fixed effects in ANOVAs, we examine both parametric and nonparametric tests for main and two-way interaction effects when the levels of each factor may be ordered or unordered.
J. C. W. Rayner, G. C. Livingston
doaj   +1 more source