C PECS 10
C ..................................................................PECS 20
C PECS 30
C SUBROUTINE PECS PECS 40
C PECS 50
C PURPOSE PECS 60
C ECONOMIZATION OF A POLYNOMIAL FOR UNSYMMETRIC RANGE PECS 70
C PECS 80
C USAGE PECS 90
C CALL PECS (P,N,BOUND,EPS,TOL,WORK) PECS 100
C PECS 110
C DESCRIPTION OF PARAMETERS PECS 120
C P - COEFFICIENT VECTOR OF GIVEN POLYNOMIAL PECS 130
C N - DIMENSION OF COEFFICIENT VECTOR PECS 140
C BOUND - RIGHT HAND BOUNDARY OF INTERVAL PECS 150
C EPS - INITIAL ERROR BOUND PECS 160
C TOL - TOLERANCE FOR ERROR PECS 170
C WORK - WORKING STORAGE OF DIMENSION N PECS 180
C PECS 190
C REMARKS PECS 200
C THE INITIAL COEFFICIENT VECTOR P IS REPLACED BY THE PECS 210
C ECONOMIZED VECTOR. PECS 220
C THE INITIAL ERROR BOUND EPS IS REPLACED BY A FINAL PECS 230
C ERROR BOUND. PECS 240
C N IS REPLACED BY THE DIMENSION OF THE REDUCED POLYNOMIAL. PECS 250
C IN CASE OF AN ARBITRARY INTERVAL (XL,XR) IT IS NECESSARY PECS 260
C FIRST TO CALCULATE THE EXPANSION OF THE GIVEN POLYNOMIAL PECS 270
C WITH ARGUMENT X IN POWERS OF T = (X-XL). PECS 280
C THIS IS ACCOMPLISHED THROUGH SUBROUTINE PCLD. PECS 290
C OPERATION IS BYPASSED IN CASE OF N LESS THAN 1. PECS 300
C PECS 310
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED PECS 320
C NONE PECS 330
C PECS 340
C METHOD PECS 350
C SUBROUTINE PECS TAKES AN (N-1)ST DEGREE POLYNOMIAL PECS 360
C APPROXIMATION TO A FUNCTION F(X) VALID WITHIN A TOLERANCE PECS 370
C EPS OVER THE INTERVAL (0,BOUND) AND REDUCES IT IF POSSIBLE PECS 380
C TO A POLYNOMIAL OF LOWER DEGREE VALID WITHIN TOLERANCE PECS 390
C TOL. PECS 400
C THE COEFFICIENT VECTOR OF THE N-TH SHIFTED CHEBYSHEV PECS 410
C POLYNOMIAL IS CALCULATED FROM THE RECURSION FORMULA PECS 420
C A(K) = -A(K+1)*K*L*(2*K-1)/(2*(N+K-1)*(N-K+1)). PECS 430
C REFERENCE PECS 440
C K. A. BRONS, ALGORITHM 37, TELESCOPE 1, CACM VOL. 4, 1961, PECS 450
C NO. 3, PP. 151. PECS 460
C PECS 470
C ..................................................................PECS 480
C PECS 490
SUBROUTINE PECS(P,N,BOUND,EPS,TOL,WORK) PECS 500
C PECS 510
DIMENSION P(1),WORK(1) PECS 520
FL=BOUND*0.5 PECS 530
C PECS 540
C TEST OF DIMENSION PECS 550
C PECS 560
1 IF(N-1)2,3,6 PECS 570
2 RETURN PECS 580
3 IF(EPS+ABS(P(1))-TOL)4,4,5 PECS 590
4 N=0 PECS 600
EPS=EPS+ABS(P(1)) PECS 610
5 RETURN PECS 620
C PECS 630
C CALCULATE EXPANSION OF CHEBYSHEV POLYNOMIAL PECS 640
C PECS 650
6 NEND=N-1 PECS 660
WORK(N)=-P(N) PECS 670
DO 7 J=1,NEND PECS 680
K=N-J PECS 690
FN=(NEND-1+K)*(N-K) PECS 700
FK=K*(K+K-1) PECS 710
7 WORK(K)=-WORK(K+1)*FK*FL/FN PECS 720
C PECS 730
C TEST FOR FEASIBILITY OF REDUCTION PECS 740
C PECS 750
FN=ABS(WORK(1)) PECS 760
IF(EPS+FN-TOL)8,8,5 PECS 770
C PECS 780
C REDUCE POLYNOMIAL PECS 790
C PECS 800
8 EPS=EPS+FN PECS 810
N=NEND PECS 820
DO 9 J=1,NEND PECS 830
9 P(J)=P(J)+WORK(J) PECS 840
GOTO 1 PECS 850
END PECS 860