Compute a lower bound of the 1-norm of a sparse matrix.
New in version 0.13.0.
Parameters: | A : ndarray or other linear operator
t : int, optional
itmax : int, optional
compute_v : bool, optional
compute_w : bool, optional
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Returns: | est : float
v : ndarray, optional
w : ndarray, optional
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Notes
This is algorithm 2.4 of [1].
In [2] it is described as follows. “This algorithm typically requires the evaluation of about 4t matrix-vector products and almost invariably produces a norm estimate (which is, in fact, a lower bound on the norm) correct to within a factor 3.”
References
[R194] | Nicholas J. Higham and Francoise Tisseur (2000), “A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra.” SIAM J. Matrix Anal. Appl. Vol. 21, No. 4, pp. 1185-1201. |
[R195] | Awad H. Al-Mohy and Nicholas J. Higham (2009), “A new scaling and squaring algorithm for the matrix exponential.” SIAM J. Matrix Anal. Appl. Vol. 31, No. 3, pp. 970-989. |