 
      SUBROUTINE RPQR79(NDEG,COEFF,ROOT,IERR,WORK)
C***BEGIN PROLOGUE  RPQR79
C***DATE WRITTEN   800601   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  F1A1A
C***KEYWORDS  POLYNOMIAL ROOTS,REAL,ROOTS,ZEROES,ZEROS
C***AUTHOR  VANDEVENDER, W. H., (SNLA)
C***PURPOSE  To find the zeros of a polynomial with real coefficients.
C***DESCRIPTION
C
C     This routine is an interface to an eigenvalue routine in EISPACK.
C     This interface was written by Walter H. Vandevender.
C
C     Abstract
C
C         This routine computes all roots of a polynomial with real
C         coefficients by computing the eigenvalues of the
C         companion matrix.
C
C     Description of Parameters
C         The user must dimension all arrays appearing in the call list
C              COEFF(NDEG+1),ROOT(NDEG),WORK(NDEG*NDEG+2*NDEG)
C
C      Input -
C       NDEG   degree of polynomial
C
C       COEFF  array of coeffficients in order of descending powers of
C              Z,   i.e. COEFF(1)*(Z**NDEG) + ... + COEFF(NDEG+1)
C
C       WORK   real work vector of length at least NDEG*(NDEG+2)
C
C     Output-
C       ROOT   complex vector of computed roots.
C
C       IERR   output error code
C             - normal code
C              0  means the roots were computed.
C             - abnormal codes
C              1  more than 30 QR iterations on some eigenvalue
C                 of the companion matrix
C              2  COEF(1) = 0.0
C              3  NDEG invalid (less than 0).
C***REFERENCES  (NONE)
C***ROUTINES CALLED  HQR,XERROR
C***END PROLOGUE  RPQR79
