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SUBROUTINE PECS

PURPOSE
   ECONOMIZATION OF A POLYNOMIAL FOR UNSYMMETRIC RANGE

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

DESCRIPTION OF PARAMETERS
   P	 - COEFFICIENT VECTOR OF GIVEN POLYNOMIAL
   N	 - DIMENSION OF COEFFICIENT VECTOR
   BOUND - RIGHT HAND BOUNDARY OF INTERVAL
   EPS	 - INITIAL ERROR BOUND
   TOL	 - TOLERANCE FOR ERROR
   WORK  - WORKING STORAGE OF DIMENSION N

REMARKS
   THE INITIAL COEFFICIENT VECTOR P IS REPLACED BY THE
   ECONOMIZED VECTOR.
   THE INITIAL ERROR BOUND EPS IS REPLACED BY A FINAL
   ERROR BOUND.
   N IS REPLACED BY THE DIMENSION OF THE REDUCED POLYNOMIAL.
   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-XL).
   THIS IS ACCOMPLISHED THROUGH SUBROUTINE PCLD.
   OPERATION IS BYPASSED IN CASE OF N LESS THAN 1.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   SUBROUTINE PECS TAKES AN (N-1)ST DEGREE POLYNOMIAL
   APPROXIMATION TO A FUNCTION F(X) VALID WITHIN A TOLERANCE
   EPS OVER THE INTERVAL (0,BOUND) AND REDUCES IT IF POSSIBLE
   TO A POLYNOMIAL OF LOWER DEGREE VALID WITHIN TOLERANCE
   TOL.
   THE COEFFICIENT VECTOR OF THE N-TH SHIFTED CHEBYSHEV
   POLYNOMIAL IS CALCULATED FROM THE RECURSION FORMULA
   A(K) = -A(K+1)*K*L*(2*K-1)/(2*(N+K-1)*(N-K+1)).
   REFERENCE
   K. A. BRONS, ALGORITHM 37, TELESCOPE 1, CACM VOL. 4, 1961,
   NO. 3, PP. 151.