C PECN 10
C ..................................................................PECN 20
C PECN 30
C SUBROUTINE PECN PECN 40
C PECN 50
C PURPOSE PECN 60
C ECONOMIZE A POLYNOMIAL FOR SYMMETRIC RANGE PECN 70
C PECN 80
C USAGE PECN 90
C CALL PECN (P,N,BOUND,EPS,TOL,WORK) PECN 100
C PECN 110
C DESCRIPTION OF PARAMETERS PECN 120
C P - COEFFICIENT VECTOR OF GIVEN POLYNOMIAL PECN 130
C ON RETURN P CONTAINS THE ECONOMIZED POLYNOMIAL PECN 140
C N - DIMENSION OF COEFFICIENT VECTOR P PECN 150
C ON RETURN N CONTAINS DIMENSION OF ECONOMIZED PECN 160
C POLYNOMIAL PECN 170
C BOUND - RIGHT HAND BOUNDARY OF RANGE PECN 180
C EPS - INITIAL ERROR BOUND PECN 190
C ON RETURN EPS CONTAINS AN ERROR BOUND FOR THE PECN 200
C ECONOMIZED POLYNOMIAL PECN 210
C TOL - TOLERANCE FOR ERROR PECN 220
C FINAL VALUE OF EPS MUST BE LESS THAN TOL PECN 230
C WORK - WORKING STORAGE OF DIMENSION N (STARTING VALUE PECN 240
C OF N RATHER THAN FINAL VALUE) PECN 250
C PECN 260
C REMARKS PECN 270
C THE OPERATION IS BYPASSED IN CASE OF N LESS THAN 1. PECN 280
C IN CASE OF AN ARBITRARY INTERVAL (XL,XR) IT IS NECESSARY PECN 290
C FIRST TO CALCULATE THE EXPANSION OF THE GIVEN POLYNOMIAL PECN 300
C WITH ARGUMENT X IN POWERS OF T = (X-(XR-XL)/2). PECN 310
C THIS IS ACCOMPLISHED THROUGH SUBROUTINE PCLD. PECN 320
C PECN 330
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED PECN 340
C NONE PECN 350
C PECN 360
C METHOD PECN 370
C SUBROUTINE PECN TAKES AN (N-1)ST DEGREE POLYNOMIAL PECN 380
C APPROXIMATION TO A FUNCTION F(X) VALID WITHIN A TOLERANCE PECN 390
C EPS OVER THE INTERVAL (-BOUND,BOUND) AND REDUCES IT IF PECN 400
C POSSIBLE TO A POLYNOMIAL OF LOWER DEGREE VALID WITHIN PECN 410
C THE GIVEN TOLERANCE TOL. PECN 420
C THE INITIAL COEFFICIENT VECTOR P IS REPLACED BY THE FINAL PECN 430
C VECTOR. THE INITIAL ERROR BOUND EPS IS REPLACED BY A FINAL PECN 440
C ERROR BOUND. PECN 450
C N IS REPLACED BY THE DIMENSION OF THE REDUCED POLYNOMIAL. PECN 460
C THE COEFFICIENT VECTOR OF THE N-TH CHEBYSHEV POLYNOMIAL PECN 470
C IS CALCULATED FROM THE RECURSION FORMULA PECN 480
C A(K-1)=-A(K+1)*K*L*L*(K-1)/((N+K-2)*(N-K+2)) PECN 490
C REFERENCE PECN 500
C K. A. BRONS, ALGORITHM 38, TELESCOPE 2, CACM VOL. 4, 1961, PECN 510
C NO. 3, PP. 151-152. PECN 520
C PECN 530
C ..................................................................PECN 540
C PECN 550
SUBROUTINE PECN(P,N,BOUND,EPS,TOL,WORK) PECN 560
C PECN 570
DIMENSION P(1),WORK(1) PECN 580
FL=BOUND*BOUND PECN 590
C PECN 600
C TEST OF DIMENSION PECN 610
C PECN 620
1 IF(N-1)2,3,6 PECN 630
2 RETURN PECN 640
3 IF(EPS+ABS(P(1))-TOL)4,4,5 PECN 650
4 N=0 PECN 660
EPS=EPS+ABS(P(1)) PECN 670
5 RETURN PECN 680
C PECN 690
C CALCULATE EXPANSION OF CHEBYSHEV POLYNOMIAL PECN 700
C PECN 710
6 NEND=N-2 PECN 720
WORK(N)=-P(N) PECN 730
DO 7 J=1,NEND,2 PECN 740
K=N-J PECN 750
FN=(NEND-1+K)*(NEND+3-K) PECN 760
FK=K*(K-1) PECN 770
7 WORK(K-1)=-WORK(K+1)*FK*FL/FN PECN 780
C PECN 790
C TEST FOR FEASIBILITY OF REDUCTION PECN 800
C PECN 810
IF(K-2)8,8,9 PECN 820
8 FN=ABS(WORK(1)) PECN 830
GOTO 10 PECN 840
9 FN=N-1 PECN 850
FN=ABS(WORK(2)/FN) PECN 860
10 IF(EPS+FN-TOL)11,11,5 PECN 870
C PECN 880
C REDUCE POLYNOMIAL PECN 890
C PECN 900
11 EPS=EPS+FN PECN 910
N=N-1 PECN 920
DO 12 J=K,N,2 PECN 930
12 P(J-1)=P(J-1)+WORK(J-1) PECN 940
GOTO 1 PECN 950
END PECN 960