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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
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.)

```