C DPCS 10
C ..................................................................DPCS 20
C DPCS 30
C SUBROUTINE DPECS DPCS 40
C DPCS 50
C PURPOSE DPCS 60
C ECONOMIZATION OF A POLYNOMIAL FOR UNSYMMETRIC RANGE DPCS 70
C DPCS 80
C USAGE DPCS 90
C CALL DPECS(P,N,BOUND,EPS,TOL,WORK) DPCS 100
C DPCS 110
C DESCRIPTION OF PARAMETERS DPCS 120
C P - DOUBLE PRECISION COEFFICIENT VECTOR OF GIVEN DPCS 130
C POLYNOMIAL DPCS 140
C N - DIMENSION OF COEFFICIENT VECTOR P DPCS 150
C BOUND - SINGLE PRECISION RIGHT HAND BOUNDARY OF INTERVAL DPCS 160
C EPS - SINGLE PRECISION INITIAL ERROR BOUND DPCS 170
C TOL - SINGLE PRECISION TOLERANCE FOR ERROR DPCS 180
C WORK - DOUBLE PRECISION WORKING STORAGE OF DIMENSION N DPCS 190
C DPCS 200
C REMARKS DPCS 210
C THE INITIAL COEFFICIENT VECTOR P IS REPLACED BY THE DPCS 220
C ECONOMIZED VECTOR. DPCS 230
C THE INITIAL ERROR BOUND EPS IS REPLACED BY A FINAL DPCS 240
C ERROR BOUND. DPCS 250
C N IS REPLACED BY THE DIMENSION OF THE REDUCED POLYNOMIAL. DPCS 260
C IN CASE OF AN ARBITRARY INTERVAL (XL,XR) IT IS NECESSARY DPCS 270
C FIRST TO CALCULATE THE EXPANSION OF THE GIVEN POLYNOMIAL DPCS 280
C WITH ARGUMENT X IN POWERS OF T = (X-XL). DPCS 290
C THIS IS ACCOMPLISHED THROUGH SUBROUTINE DPCLD. DPCS 300
C OPERATION IS BYPASSED IN CASE OF N LESS THAN 1. DPCS 310
C DPCS 320
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DPCS 330
C NONE DPCS 340
C DPCS 350
C METHOD DPCS 360
C SUBROUTINE DPECS TAKES AN (N-1)ST DEGREE POLYNOMIAL DPCS 370
C APPROXIMATION TO A FUNCTION F(X) VALID WITHIN A TOLERANCE DPCS 380
C EPS OVER THE INTERVAL (0,BOUND) AND REDUCES IT IF POSSIBLE DPCS 390
C TO A POLYNOMIAL OF LOWER DEGREE VALID WITHIN TOLERANCE DPCS 400
C TOL. DPCS 410
C THE COEFFICIENT VECTOR OF THE N-TH SHIFTED CHEBYSHEV DPCS 420
C POLYNOMIAL IS CALCULATED FROM THE RECURSION FORMULA DPCS 430
C A(K) = -A(K+1)*K*L*(2*K-1)/(2*(N+K-1)*(N-K+1)). DPCS 440
C REFERENCE DPCS 450
C K. A. BRONS, ALGORITHM 37, TELESCOPE 1, CACM VOL. 4, 1961, DPCS 460
C NO. 3, PP. 151. DPCS 470
C DPCS 480
C ..................................................................DPCS 490
C DPCS 500
SUBROUTINE DPECS(P,N,BOUND,EPS,TOL,WORK) DPCS 510
C DPCS 520
DIMENSION P(1),WORK(1) DPCS 530
DOUBLE PRECISION P,WORK DPCS 540
C DPCS 550
FL=BOUND*0.5 DPCS 560
C DPCS 570
C TEST OF DIMENSION DPCS 580
C DPCS 590
1 IF(N-1)2,3,6 DPCS 600
2 RETURN DPCS 610
C DPCS 620
3 IF(EPS+ABS(SNGL(P(1)))-TOL)4,4,5 DPCS 630
4 N=0 DPCS 640
EPS=EPS+ABS(SNGL(P(1))) DPCS 650
5 RETURN DPCS 660
C DPCS 670
C CALCULATE EXPANSION OF CHEBYSHEV POLYNOMIAL DPCS 680
C DPCS 690
6 NEND=N-1 DPCS 700
WORK(N)=-P(N) DPCS 710
DO 7 J=1,NEND DPCS 720
K=N-J DPCS 730
FN=(NEND-1+K)*(N-K) DPCS 740
FK=K*(K+K-1) DPCS 750
7 WORK(K)=-WORK(K+1)*DBLE(FK)*DBLE(FL)/DBLE(FN) DPCS 760
C DPCS 770
C TEST FOR FEASIBILITY OF REDUCTION DPCS 780
C DPCS 790
FN=DABS(WORK(1)) DPCS 800
IF(EPS+FN-TOL)8,8,5 DPCS 810
C DPCS 820
C REDUCE POLYNOMIAL DPCS 830
C DPCS 840
8 EPS=EPS+FN DPCS 850
N=NEND DPCS 860
DO 9 J=1,NEND DPCS 870
9 P(J)=P(J)+WORK(J) DPCS 880
GOTO 1 DPCS 890
END DPCS 900