Efficient Algorithms and Error Analysis for the Modified Nystrom Method
نویسندگان
چکیده
Lemma 8. Given an m × m symmetric matrix A and a target rank k, we let C1 contain the c1 columns of A selected by a column sampling algorithm such that the following inequality holds: ∥∥A− PC1A∥∥2F ≤ f∥∥A−Ak∥∥2F . Then we select c2 = kf −1 columns to construct C2 and c3 = (c1+ c2) −1 columns to construct C3, both using the adaptive sampling according to the residual B1 = A − PC1A and B2 = A − P[C1,C2]A, respectively. Let C = [C1,C2,C3], we have that
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