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decuslib20-02
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decus/20-0026/dse35.doc
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SUBROUTINE DSE35
PURPOSE
TO COMPUTE A VECTOR OF SMOOTHED FUNCTION VALUES GIVEN A
VECTOR OF FUNCTION VALUES WHOSE ENTRIES CORRESPOND TO
EQUIDISTANTLY SPACED ARGUMENT VALUES.
USAGE
CALL DSE35(Y,Z,NDIM,IER)
DESCRIPTION OF PARAMETERS
Y - GIVEN VECTOR OF DOUBLE PRECISION FUNCTION VALUES
(DIMENSION NDIM)
Z - RESULTING VECTOR OF DOUBLE PRECISION SMOOTHED
FUNCTION VALUES (DIMENSION NDIM)
NDIM - DIMENSION OF VECTORS Y AND Z
IER - RESULTING ERROR PARAMETER
IER = -1 - NDIM IS LESS THAN 5
IER = 0 - NO ERROR
REMARKS
(1) IF IER=-1 THERE HAS BEEN NO COMPUTATION.
(2) Z CAN HAVE THE SAME STORAGE ALLOCATION AS Y. IF Y IS
DISTINCT FROM Z, THEN IT IS NOT DESTROYED.
SUBROUTINE AND FUNCTION SUBPROGRAMS REQUIRED
NONE
METHOD
IF X IS THE (SUPPRESSED) VECTOR OF ARGUMENT VALUES, THEN
EXCEPT AT THE POINTS X(1),X(2),X(NDIM-1) AND X(NDIM), EACH
SMOOTHED VALUE Z(I) IS OBTAINED BY EVALUATING AT X(I) THE
LEAST-SQUARES POLYNOMIAL OF DEGREE 3 RELEVANT TO THE 5
SUCCESSIVE POINTS (X(I+K),Y(I+K)) K = -2,-1,...,2. (SEE
HILDEBRAND, F.B., INTRODUCTION TO NUMERICAL ANALYSIS,
MC GRAW-HILL, NEW YORK/TORONTO/LONDON, 1956, PP. 295-302.)