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dash_svd(A, k[, p_max, s, tol])

A Julia implementation of the dynamic shifts-based randomized SVD (dashSVD) with PVE accuracy control for a matrix A of rank k.

Parameters:

• A: the input matrix of size (m, n)
• k: the target rank of truncated SVD, k ≤ min(m,n)
• p_max: the upper bound of power parameter p, default = 1000
• s: the oversampling parameter, min(m,n) ≥ k + s, default = k/2
• tol:the error tolerance for PVE, default = 1e-2

Returns:

• U: the matrix of size (m, k) containing the first k left singular vectors of A
• S: the vector of size (k, ) containing the k largest singular values of A in ascending order
• V: the matrix of size (n, k) containing the first k right singular vectors of A

Examples

julia> A = randn(10, 6)
julia> U, S, V = dash_svd(A, 2)

[U, S, V] = eig_svd(A) for m >= n, using eigen(A'*A)