PDP-10 Archive: decus/20-0026/csps.doc from decuslib20-02

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SUBROUTINE CSPS

PURPOSE
   COMPUTES THE VALUE OF AN N-TERM EXPANSION IN SHIFTED
   CHEBYSHEV POLYNOMIALS WITH COEFFICIENT VECTOR C
   FOR ARGUMENT VALUE X.

USAGE
   CALL CSPS(Y,X,C,N)

DESCRIPTION OF PARAMETERS
   Y	 - RESULT VALUE
   X	 - ARGUMENT VALUE
   C	 - COEFFICIENT VECTOR OF GIVEN EXPANSION
	   COEFFICIENTS ARE ORDERED FROM LOW TO HIGH
   N	 - DIMENSION OF COEFFICIENT VECTOR C

REMARKS
   OPERATION IS BYPASSED IN CASE N LESS THAN 1

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   DEFINITION
   Y=SUM(C(I)*TS(I-1,X), SUMMED OVER I FROM 1 TO N).
   EVALUATION IS DONE BY MEANS OF BACKWARD RECURSION
   USING THE RECURRENCE EQUATION FOR SHIFTED
   CHEBYSHEV POLYNOMIALS
   TS(N+1,X)=(4*X-2)*TS(N,X)-TS(N-1,X).