SLATEC Routines --- RPZERO ---

*DECK RPZERO
      SUBROUTINE RPZERO (N, A, R, T, IFLG, S)
C***BEGIN PROLOGUE  RPZERO
C***PURPOSE  Find the zeros of a polynomial with real coefficients.
C***LIBRARY   SLATEC
C***CATEGORY  F1A1A
C***TYPE      SINGLE PRECISION (RPZERO-S, CPZERO-C)
C***KEYWORDS  POLYNOMIAL ROOTS, POLYNOMIAL ZEROS, REAL ROOTS
C***AUTHOR  Kahaner, D. K., (NBS)
C***DESCRIPTION
C
C      Find the zeros of the real polynomial
C         P(X)= A(1)*X**N + A(2)*X**(N-1) +...+ A(N+1)
C
C    Input...
C       N = degree of P(X)
C       A = real vector containing coefficients of P(X),
C            A(I) = coefficient of X**(N+1-I)
C       R = N word complex vector containing initial estimates for zeros
C            if these are known.
C       T = 6(N+1) word array used for temporary storage
C       IFLG = flag to indicate if initial estimates of
C              zeros are input.
C            If IFLG .EQ. 0, no estimates are input.
C            If IFLG .NE. 0, the vector R contains estimates of
C               the zeros
C       ** Warning ****** If estimates are input, they must
C                         be separated; that is, distinct or
C                         not repeated.
C       S = an N word array
C
C    Output...
C       R(I) = ith zero,
C       S(I) = bound for R(I) .
C       IFLG = error diagnostic
C    Error Diagnostics...
C       If IFLG .EQ. 0 on return, all is well.
C       If IFLG .EQ. 1 on return, A(1)=0.0 or N=0 on input.
C       If IFLG .EQ. 2 on return, the program failed to converge
C                after 25*N iterations.  Best current estimates of the
C                zeros are in R(I).  Error bounds are not calculated.
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  CPZERO
C***REVISION HISTORY  (YYMMDD)
C   810223  DATE WRITTEN
C   890206  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C***END PROLOGUE  RPZERO