SLATEC Routines --- RPQR79 ---

*DECK RPQR79
      SUBROUTINE RPQR79 (NDEG, COEFF, ROOT, IERR, WORK)
C***BEGIN PROLOGUE  RPQR79
C***PURPOSE  Find the zeros of a polynomial with real coefficients.
C***LIBRARY   SLATEC
C***CATEGORY  F1A1A
C***TYPE      SINGLE PRECISION (RPQR79-S, CPQR79-C)
C***KEYWORDS  COMPLEX POLYNOMIAL, POLYNOMIAL ROOTS, POLYNOMIAL ZEROS
C***AUTHOR  Vandevender, W. H., (SNLA)
C***DESCRIPTION
C
C   Abstract
C       This routine computes all zeros of a polynomial of degree NDEG
C       with real 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))
C
C    --Input--
C      NDEG    degree of polynomial
C
C      COEFF   REAL coefficients in descending order.  i.e.,
C              P(Z)= COEFF(1)*(Z**NDEG) + COEFF(NDEG)*Z + COEFF(NDEG+1)
C
C      WORK    REAL work array of dimension at least NDEG*(NDEG+2)
C
C   --Output--
C      ROOT    COMPLEX vector of 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 of the
C             companion matrix
C          2  COEFF(1)=0.0
C          3  NDEG is invalid (less than or equal to 0)
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  HQR, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   800601  DATE WRITTEN
C   890505  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
C   911010  Code reworked and simplified.  (RWC and WRB)
C***END PROLOGUE  RPQR79