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SUBROUTINE PQFB

PURPOSE
   TO FIND AN APPROXIMATION Q(X)=Q1+Q2*X+X*X TO A QUADRATIC
   FACTOR OF A GIVEN POLYNOMIAL P(X) WITH REAL COEFFICIENTS.

USAGE
   CALL PQFB(C,IC,Q,LIM,IER)

DESCRIPTION OF PARAMETERS
   C   - INPUT VECTOR CONTAINING THE COEFFICIENTS OF P(X) -
	 C(1) IS THE CONSTANT TERM (DIMENSION IC)
   IC  - DIMENSION OF C
   Q   - VECTOR OF DIMENSION 4 - ON INPUT Q(1) AND Q(2) MUST
	 CONTAIN INITIAL GUESSES FOR Q1 AND Q2 - ON RETURN Q(1)
	 AND Q(2) CONTAIN THE REFINED COEFFICIENTS Q1 AND Q2 OF
	 Q(X), WHILE Q(3) AND Q(4) CONTAIN THE COEFFICIENTS A
	 AND B OF A+B*X, WHICH IS THE REMAINDER OF THE QUOTIENT
	 OF P(X) BY Q(X)
   LIM - INPUT VALUE SPECIFYING THE MAXIMUM NUMBER OF
	 ITERATIONS TO BE PERFORMED
   IER - RESULTING ERROR PARAMETER (SEE REMARKS)
	 IER= 0 - NO ERROR
	 IER= 1 - NO CONVERGENCE WITHIN LIM ITERATIONS
	 IER=-1 - THE POLYNOMIAL P(X) IS CONSTANT OR UNDEFINED
		  - OR OVERFLOW OCCURRED IN NORMALIZING P(X)
	 IER=-2 - THE POLYNOMIAL P(X) IS OF DEGREE 1
	 IER=-3 - NO FURTHER REFINEMENT OF THE APPROXIMATION TO
		  A QUADRATIC FACTOR IS FEASIBLE, DUE TO EITHER
		  DIVISION BY 0, OVERFLOW OR AN INITIAL GUESS
		  THAT IS NOT SUFFICIENTLY CLOSE TO A FACTOR OF
		  P(X)

REMARKS
   (1)	IF IER=-1 THERE IS NO COMPUTATION OTHER THAN THE
	POSSIBLE NORMALIZATION OF C.
   (2)	IF IER=-2 THERE IS NO COMPUTATION OTHER THAN THE
	NORMALIZATION OF C.
   (3)	IF IER =-3  IT IS SUGGESTED THAT A NEW INITIAL GUESS BE
	MADE FOR A QUADRATIC FACTOR.  Q, HOWEVER, WILL CONTAIN
	THE VALUES ASSOCIATED WITH THE ITERATION THAT YIELDED
	THE SMALLEST NORM OF THE MODIFIED LINEAR REMAINDER.
   (4)	IF IER=1, THEN, ALTHOUGH THE NUMBER OF ITERATIONS LIM
	WAS TOO SMALL TO INDICATE CONVERGENCE, NO OTHER PROB-
	LEMS HAVE BEEN DETECTED, AND Q WILL CONTAIN THE VALUES
	ASSOCIATED WITH THE ITERATION THAT YIELDED THE SMALLEST
	NORM OF THE MODIFIED LINEAR REMAINDER.
   (5)	FOR COMPLETE DETAIL SEE THE DOCUMENTATION FOR
	SUBROUTINES PQFB AND DPQFB.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   COMPUTATION IS BASED ON BAIRSTOW'S ITERATIVE METHOD.  (SEE
   WILKINSON, J.H., THE EVALUATION OF THE ZEROS OF ILL-CON-
   DITIONED POLYNOMIALS (PART ONE AND TWO), NUMERISCHE MATHE-
   MATIK, VOL.1 (1959), PP. 150-180, OR HILDEBRAND, F.B.,
   INTRODUCTION TO NUMERICAL ANALYSIS, MC GRAW-HILL, NEW YORK/
   TORONTO/LONDON, 1956, PP. 472-476.)