Results 11 to 20 of about 3,729,724 (366)
Exploiting Constant Trace Property in Large-scale Polynomial Optimization [PDF]
ACM Transactions on Mathematical Software, 2022 We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP). As a result, such moment relaxations
Ngoc Hoang Anh +3 more
openalex +3 more sources
Lebesgue functions and Lebesgue constants in polynomial interpolation [PDF]
Journal of Inequalities and Applications, 2016 The Lebesgue constant is a valuable numerical instrument for linear interpolation because it provides a measure of how close the interpolant of a function is to the best polynomial approximant of the function.
Bayram Ali Ibrahimoglu
doaj +5 more sources
Determining projection constants of univariate polynomial spaces [PDF]
Journal of Approximation Theory, 2018 The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a linear program, and the lower bound, produced by a semidefinite program exploiting the method of moments, are often ...
Simon Foucart, Jean B. Lasserre
openalex +6 more sources
Convergence for score-based generative modeling with polynomial complexity [PDF]
Neural Information Processing Systems, 2022 Score-based generative modeling (SGM) is a highly successful approach for learning a probability distribution from data and generating further samples. We prove the first polynomial convergence guarantees for the core mechanic behind SGM: drawing samples
Holden Lee, Jianfeng Lu, Yixin Tan
semanticscholar +1 more source
Learning Quantum Hamiltonians at Any Temperature in Polynomial Time [PDF]
Symposium on the Theory of Computing, 2023 We study the problem of learning a local quantum Hamiltonian H given copies of its Gibbs state ρ = e−β H/(e−β H) at a known inverse temperature β>0. Anshu, Arunachalam, Kuwahara, and Soleimanifar gave an algorithm to learn a Hamiltonian on n qubits to ...
Ainesh Bakshi +3 more
semanticscholar +1 more source
Multivariate trace estimation in constant quantum depth [PDF]
Quantum, 2022 There is a folkloric belief that a depth-Θ(m) quantum circuit is needed to estimate the trace of the product of m density matrices (i.e., a multivariate trace), a subroutine crucial to applications in condensed matter and quantum information science.
Yihui Quek, M. Wilde, Eneet Kaur
semanticscholar +1 more source
Asymptotics of Polynomial Interpolation and the Bernstein Constants [PDF]
Results in Mathematics, 2021 AbstractIt is well known that the interpolation error for $$\left| x\right| ^{\alpha },\alpha >0$$ x α , α > 0
Michael Revers
openalex +4 more sources
Learning Read-Constant Polynomials of Constant Degree Modulo Composites [PDF]
Theory of Computing Systems, 2011 Peer ...
Chattopadhyay, Arkadev +3 more
openaire +5 more sources
Is Catalan’s Constant Rational?
Mathematics, 2022 This paper employs a contour integral method to derive and evaluate the infinite sum of the Euler polynomial expressed in terms of the Hurwitz Zeta function. We provide formulae for several classes of infinite sums of the Euler polynomial in terms of the
Robert Reynolds, Allan Stauffer
doaj +1 more source
Homogeneous Polynomial Solutions to Constant Coefficient PDE's
Advances in Mathematics, 1996 Given any field \(K\) and a polynomial \(p\in K[X]= K[X_1,\dots,X_n]\), the differential operator \(p(D)\) on \(K[X]\) is defined by substituting \(\partial/\partial x_i\) for the variable \(X_i\). For the case that \(K\) is algebraically closed for characteristic 0, and \(p\) is homogeneous, the set of homogeneous solutions of the PDE \(p(D)=0\) is ...
B. Reznick
semanticscholar +2 more sources