SLACON - estimate 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 SLA­
              CON must be re-called with all the other parameters
              unchanged.

       ISGN   (workspace) INTEGER array, dimension (N)

       EST    (output) REAL
              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.



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