When a system of real quadratic equations has a solution
نویسندگان
چکیده
We provide a sufficient condition for solvability of system real quadratic equations pi(x)=yi, i=1,…,m, where pi:Rn⟶R are forms. By solving positive semidefinite program, one can reduce it to another the type qi(x)=αi, qi:Rn⟶R forms and αi=traceqi. prove that latter has solution x∈Rn if some (equivalently, any) orthonormal basis A1,…,Am in space spanned by matrices qi, operator norm A12+…+Am2 does not exceed η/m absolute constant η>0. The be checked polynomial time is satisfied, example, random qi provided m≤γn an γ>0. similar homogeneous have non-trivial solution. While we obtain algebraic nature, proof relies on analytic tools including Fourier analysis measure concentration.
منابع مشابه
a study on construction of iranian life tables: the case study of modified brass logit system
چکیده ندارد.
15 صفحه اولA Legendre-spectral scheme for solution of nonlinear system of Volterra-Fredholm integral equations
This paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.
متن کاملNumerical solution of a system of fuzzy polynomial equations by modified Adomian decomposition method
In this paper, we present some efficient numerical algorithm for solving system of fuzzy polynomial equations based on Newton's method. The modified Adomian decomposition method is applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms.
متن کاملsolution of security constrained unit commitment problem by a new multi-objective optimization method
چکیده-پخش بار بهینه به عنوان یکی از ابزار زیر بنایی برای تحلیل سیستم های قدرت پیچیده ،برای مدت طولانی مورد بررسی قرار گرفته است.پخش بار بهینه توابع هدف یک سیستم قدرت از جمله تابع هزینه سوخت ،آلودگی ،تلفات را بهینه می کند،و هم زمان قیود سیستم قدرت را نیز برآورده می کند.در کلی ترین حالتopf یک مساله بهینه سازی غیر خطی ،غیر محدب،مقیاس بزرگ،و ایستا می باشد که می تواند شامل متغیرهای کنترلی پیوسته و گ...
ذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2022
ISSN: ['1857-8365', '1857-8438']
DOI: https://doi.org/10.1016/j.aim.2022.108391