Analyticity of Parametric Elliptic Eigenvalue Problems and Applications to Quasi-Monte Carlo Methods

2022/02/05 by Nguyen, Van Kien · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2202.02530

Abstract

In the present paper, we study the analyticity of the leftmost eigenvalue of the linear elliptic partial differential operator with random coefficient and analyze the convergence rate of the quasi-Monte Carlo method for approximation of the expectation of this quantity. The random coefficient is assumed to be represented by an affine expansion a₀(\boldsymbolx)+∑_{j∈ ℕ}y_ja_j(\boldsymbolx), where elements of the parameter vector \boldsymboly=(y_j)_{j∈ ℕ}∈ U^∞ are independent and identically uniformly distributed on U:=[-(1)/(2),(1)/(2)]. Under the assumption ‖∑_{j∈ ℕ}ρ_j|a_j|‖_{L_∞(D)}

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