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Version 1.1.0

3rd December 2009

MF71: Unsymmetric matrix: estimate 1-norm

This subroutine estimates the 1-norm (\(\max _ j \sum _{ i=1} ^ n | a _{ij}|\)) of an \(n \times n\) complex matrix \(\mathbf{ A}\) given the ability to multiply a vector by both the matrix and its conjugate transpose. Because the explicit form of \(\mathbf{ A}\) is not required, the subroutine can be used for estimating the norm of matrix functions such as the inverse. Additionally this subroutine is potentially useful for estimating condition numbers of a matrix when the matrix is sparse or not available explicitly.