`scipy.optimize._trustregion_exact:estimate_smallest_singular_value`

source: /scipy/optimize/_trustregion_exact.py :48

Signature

def estimate_smallest_singular_value ( U )

Summary

Given upper triangular matrix U estimate the smallest singular value and the correspondent right singular vector in O(n**2) operations.

Parameters

U : ndarray: Square upper triangular matrix.

Returns

s_min : float: Estimated smallest singular value of the provided matrix.
z_min : ndarray: Estimated right singular vector.

Notes

The procedure is based on ^[1] and is done in two steps. First, it finds a vector e with components selected from {+1, -1} such that the solution w from the system U.T w = e is as large as possible. Next it estimate U v = w. The smallest singular value is close to norm(w)/norm(v) and the right singular vector is close to v/norm(v).

The estimation will be better more ill-conditioned is the matrix.

Aliases

scipy.optimize._trustregion_exact.estimate_smallest_singular_value