imsl.linalg.lu_cond

lu_cond(a)

Compute the \(L_1\) norm condition number of a matrix.

Parameters:a ((N,N) array_like) – Array containing the matrix. Returns:The \(L_1\) condition number of a. Return type:*float*

Notes

The \(L_1\) condition number of a matrix A is defined as \(\kappa(A)=||A||_1||A^{-1}||_1\). Its computation uses the same algorithm as in [1]. If the estimated condition number is greater than \(1/\epsilon\) (where \(\epsilon\) is the machine precision), a warning message is issued. This indicates that very small changes in A may produce large changes in the solution x of a linear system Ax = b.

This function creates a temporary LU() instance and calls method LU.cond() on that instance.

References

[1]	Dongarra, J.J., J.R. Bunch, C.B. Moler, and G.W. Stewart (1979), LINPACK User’s Guide, SIAM, Philadelphia.