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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.

```