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SUBROUTINE TEAS

PURPOSE
   CALCULATE THE LIMIT OF A GIVEN SEQUENCE BY MEANS OF THE
   EPSILON-ALGORITHM.

USAGE
   CALL TEAS(X,N,FIN,EPS,IER)

DESCRIPTION OF PARAMETERS
   X	  - VECTOR WHOSE COMPONENTS ARE TERMS OF THE GIVEN
	    SEQUENCE. ON RETURN THE COMPONENTS OF VECTOR X
	    ARE DESTROYED.
   N	  - DIMENSION OF INPUT VECTOR X.
   FIN	  - RESULTANT SCALAR CONTAINING ON RETURN THE LIMIT
	    OF THE GIVEN SEQUENCE.
   EPS	  - AN INPUT VALUE, WHICH SPECIFIES THE UPPER BOUND
	    OF THE RELATIVE (ABSOLUTE) ERROR IF THE COMPONENTS
	    OF X ARE ABSOLUTELY GREATER (LESS) THAN ONE.
	    CALCULATION IS TERMINATED AS SOON AS THREE TIMES IN
	    SUCCESSION THE RELATIVE (ABSOLUTE) DIFFERENCE
	    BETWEEN NEIGHBOURING TERMS IS NOT GREATER THAN EPS.
   IER	  - RESULTANT ERROR PARAMETER CODED IN THE FOLLOWING
	    FORM
	     IER=0  - NO ERROR
	     IER=1  - REQUIRED ACCURACY NOT REACHED WITH
		      MAXIMAL NUMBER OF ITERATIONS
	     IER=-1 - INTEGER N IS LESS THAN TEN.

REMARKS
   NO ACTION BESIDES ERROR MESSAGE IN CASE N LESS THAN TEN.
   THE CHARACTER OF THE GIVEN INFINITE SEQUENCE MUST BE
   RECOGNIZABLE BY THOSE N COMPONENTS OF THE INPUT VECTOR X.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   THE CONVERGENCE OF THE GIVEN SEQUENCE IS ACCELERATED BY
   MEANS OF THE E(2)-TRANSFORMATION, USED IN AN ITERATIVE WAY.
   FOR REFERENCE, SEE
   ALGORITHM 215,SHANKS, CACM 1963, NO. 11, PP. 662. AND
   P. WYNN, SINGULAR RULES FOR CERTAIN NON-LINEAR ALGORITHMS
   BIT VOL. 3, 1963, PP. 175-195.