rpqr79.f
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