NAME¶

SLACON - estimates the 1-norm of a square, real matrix A

SYNOPSIS¶

SUBROUTINE SLACON(

N, V, X, ISGN, EST, KASE )

INTEGER KASE, N REAL EST INTEGER ISGN( * ) REAL V( * ), X( * )

PURPOSE¶

SLACON estimates the 1-norm of a square, real matrix A. Reverse communication is used for evaluating matrix-vector products.

ARGUMENTS¶

N (input) INTEGER

The order of the matrix. N >= 1.

V (workspace) REAL array, dimension (N)

On the final return, V = A*W, where EST = norm(V)/norm(W) (W is not returned).

X (input/output) REAL array, dimension (N)

On an intermediate return, X should be overwritten by A * X, if KASE=1, A' * X, if KASE=2, and SLACON must be re-called with all the other parameters unchanged.

ISGN (workspace) INTEGER array, dimension (N)

EST (input/output) REAL

On entry with KASE = 1 or 2 and JUMP = 3, EST should be unchanged from the previous call to SLACON. On exit, EST is an estimate (a lower bound) for norm(A).

KASE (input/output) INTEGER

On the initial call to SLACON, KASE should be 0. On an intermediate return, KASE will be 1 or 2, indicating whether X should be overwritten by A * X or A' * X. On the final return from SLACON, KASE will again be 0.

FURTHER DETAILS¶

Contributed by Nick Higham, University of Manchester.
Originally named SONEST, dated March 16, 1988.
Reference: 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., vol. 14, no. 4, pp. 381-396, December 1988.