When k approaches one of λ_i, the solution u will approach an eigenfunction. Define the smallest, relative distance between k~2 and λ_i by δ = min_i∣(k~2-λ_i)/(k~2)∣. Since when δ > 0 the solution u of (2) can be obtained by the BAMs. we may choose k~2 so as to approach the eigenvalue λ_l we want. As a consequence, the solution from the BAMs is an approximate eigenfunction φ_l.
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