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SUBROUTINE PECN

PURPOSE
   ECONOMIZE A POLYNOMIAL FOR SYMMETRIC RANGE

USAGE
   CALL PECN (P,N,BOUND,EPS,TOL,WORK)

DESCRIPTION OF PARAMETERS
   P	 - COEFFICIENT VECTOR OF GIVEN POLYNOMIAL
	   ON RETURN P CONTAINS THE ECONOMIZED POLYNOMIAL
   N	 - DIMENSION OF COEFFICIENT VECTOR P
	   ON RETURN N CONTAINS DIMENSION OF ECONOMIZED
	   POLYNOMIAL
   BOUND - RIGHT HAND BOUNDARY OF RANGE
   EPS	 - INITIAL ERROR BOUND
	   ON RETURN EPS CONTAINS AN ERROR BOUND FOR THE
	   ECONOMIZED POLYNOMIAL
   TOL	 - TOLERANCE FOR ERROR
	   FINAL VALUE OF EPS MUST BE LESS THAN TOL
   WORK  - WORKING STORAGE OF DIMENSION N (STARTING VALUE
	   OF N RATHER THAN FINAL VALUE)

REMARKS
   THE OPERATION IS BYPASSED IN CASE OF N LESS THAN 1.
   IN CASE OF AN ARBITRARY INTERVAL (XL,XR) IT IS NECESSARY
   FIRST TO CALCULATE THE EXPANSION OF THE GIVEN POLYNOMIAL
   WITH ARGUMENT X IN POWERS OF T = (X-(XR-XL)/2).
   THIS IS ACCOMPLISHED THROUGH SUBROUTINE PCLD.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   SUBROUTINE PECN TAKES AN (N-1)ST DEGREE POLYNOMIAL
   APPROXIMATION TO A FUNCTION F(X) VALID WITHIN A TOLERANCE
   EPS OVER THE INTERVAL (-BOUND,BOUND) AND REDUCES IT IF
   POSSIBLE TO A POLYNOMIAL OF LOWER DEGREE VALID WITHIN
   THE GIVEN TOLERANCE TOL.
   THE INITIAL COEFFICIENT VECTOR P IS REPLACED BY THE FINAL
   VECTOR. THE INITIAL ERROR BOUND EPS IS REPLACED BY A FINAL
   ERROR BOUND.
   N IS REPLACED BY THE DIMENSION OF THE REDUCED POLYNOMIAL.
   THE COEFFICIENT VECTOR OF THE N-TH CHEBYSHEV POLYNOMIAL
   IS CALCULATED FROM THE RECURSION FORMULA
   A(K-1)=-A(K+1)*K*L*L*(K-1)/((N+K-2)*(N-K+2))
   REFERENCE
   K. A. BRONS, ALGORITHM 38, TELESCOPE 2, CACM VOL. 4, 1961,
   NO. 3, PP. 151-152.