skeel

SKEEL(A) estimates Skeel's condition number, NORM(ABS(INV(A))*ABS(A), INF), without computing ABS(INV(A))*ABS(A). SKEEL(A) is always less than or equal to COND(A, INF). In practice, SKEEL(A) can be much less than COND(A, INF). SKEEL(A) is invariant to row scaling.

SKEEL(A, P) directly computes Skeel's condition number in the P-norm: NORM(ABS(INV(A))*ABS(A), P).

Example:

A = [1 0; 0 1e9];
cond(A) % = 1e9
skeel(A) % = 1

References:

[1] Robert D. Skeel, "Scaling for numerical stability in Gaussian elimination", J. ACM, 26 (1979), pp. 494-526.

[2] N.J. Higham, "FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., 14 (1988), pp. 381-396.