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What is the complexity of weakly singular integral equations?

2012

Consider the integral equation where ν ∈ (0, 1), f ∈ C m [0, 1], a, b ∈ C 2m ([0, 1]×[0, 1]), m ∈ N, and the corresponding homogeneous equation has only the trivial solution. By a fast (C, C m ) solver of (1) we mean a solver which produces approximate solutions u n , n ∈ N, such that • given the values of a, b and f at certain not more than n points depending on the solver (with n → ∞ as n → ∞), the parameters of u n can be determined at the cost of γ m n arithmetical operations, and an

doi:10.1063/1.4756232
fatcat:xdv76f4ohrahthg6jmsbnlf3yi