Results 1 to 10 of about 3,572,424 (305)
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
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Polynomial solutions to constant coefficient differential equations [PDF]
Transactions of the American Mathematical Society, 1992 Let D 1 , … , D r ∈ C [ ∂ / ∂ x 1 , … , ∂ / ∂
Paul Smith, S. P. Smith
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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
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Relating polynomial time to constant depth
Theoretical Computer Science, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
H. Vollmer
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Definability by constant-depth polynomial-size circuits
Information and Control, 1986 A class \(\Sigma\) of \(\sigma\)-structures is called circuit definable if there is a constant-depth, polynomial-size bounded sequence \(C_1, \ldots, C_n,\ldots\) of circuits, where each \(C_n\) is symmetric and accepts a structure \(S\) on the universe \(U_n=\{0,\ldots, n-1\}\) iff \(S\in \Sigma\).
Denenberg, Larry +2 more
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Constant terms in powers of a Laurent polynomial
Indagationes Mathematicae, 1998 The following is a conjecture of O. Mathieu: Let \(K\) be a connected real compact Lie group. Let \(f\) and \(g\) be \(K\)-finite functions on \(K\). Assume for all \(n \geq 1\) that the constant term of \(f^{n}\) vanishes, i.e. \[ \int_{K} f^{n}(k) \;dk = 0 .
Duistermaat, J.J., Kallen, W. van der
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MOTION PLANNING BY PIECEWISE CONSTANT OR POLYNOMIAL INPUTS
IFAC Proceedings Volumes, 1992 Abstract In this paper we present an algorithmic solution of the “Exact Motion Planning Problem” for nilpotent systems, by piecewise constant or polynomial inputs. By using an identification process, we improve here the solution earlier given by Lafferiere and Sussmann, for systems without drift. So we obtain a much smaller number of pieces (in case
G. Jacob
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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
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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
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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
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