lit
    JINRLIB

CHEB -

E221

: I.Barrodale, C.Phillips :

popaa ao co aco p popo cc pa e221_2, .. ao op e221_1, p

e221

:

: - SUBROUTINE
: - CHEB

:

CALL CHEB(M,N,MDIM,NDIM,A,B,TOL,RELERR,X,IRANK,RESMAX,ITER,ICODE), :

M - (INTEGER) co pa m.
N - (INTEGER) co c n, n ≤ m.
MDIM - (INTEGER) opa papoc acca A, MDIM ≥ m+1.
NDIM - (INTEGER) pa papoc acca A, NDIM ≥ n+3.
A - (REAL*8) p acc. a o A cop pacopoa ap oo, .. A(i,j)=aij.
opo A oac c.
B - (REAL*8) oop acc ≥ m+1.
a o p m o B o copa op e221_3.
copa ci.
TOL - (REAL*8) apap , oop o pa , coo o ao ooc (app, 1.0-14 REAL*8).
RELERR - (REAL*8) a o RELERR oaa pa 0.0D0, c pc co p.
RELERR, 0.D0 - c. aa 1.
X - (REAL*8) oop acc ≥ n+3.
a o p n o X cop op p e221_1.
IRANK - (INTEGER) a o IRANK cop o paa ap (a oa o ac o TOL).
RESMAX - (REAL*8) a o RESMAX cop a acao .
ITER - (INTEGER) a o ITER cop co o -pa.
ICODE - (INTEGER) oo apap:
ICODE=0 - p e221_1 co,
ICODE=1 - p e221_1 co,
ICODE=2 - c aoo ppo -a o op.

:

coc opoa cc-o oo popapoa po aco aa.

:

  1. c a o RELERR cop o ooo a r, o a o RELERR copc r'< r, X - co p e221_1', RESMAX - acaa a c', aa o (c'-c)/c < r', c - acaa a, cooca co p e221_1. RELERR (app, RELERR=0.1D0), co cc-pa oo copaac.
  2. c RESMAX pa o ooo o opo TOL, o c copa coo aa p o pa , c RESMAX < TOL.

:

  1. I.Barrodal, C.Phillips, Algorithm 495: Solution of an overdetermined system of linear quations in the Chbyshv norm, ACM Trans. Math. Software 1 (1975) 264-270.
:
     cc 6 pa c 2 c  oo pao ac:
 
        +  = 1       + 2  = 1      + 3  = 2
        1   2          1     2         1     2
        + 4  = 2     + 5  = 3      + 6  = 3
        1     2        1     2         1     2
 
       . . .
       IMPLICIT REAL*8 (A-H,O-Z)
       DIMENSION A(5,7),B(7),X(5)
       DATA B/1.0D0,1.0D0,2.0D0,2.0D0,3.0D0,3.0D0,0.0D0/
       DO 3 I=1,6
       A(1,I)=1.0D0
    3  A(2,I)=I
       TOL=1.0D-11
       RELERR=0.0D0
       CALL CHEB(6,2,7,5,A,B,TOL,RELERR,X,IRANK,RESMAX,ITER,ICODE)
       . . .
:
       X(1)=  .25   X(2)=  .50   IRANK=  2
       ITER=  3   ICODE=  1  RESMAX=  .25


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