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decus/20-0026/det3.doc
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SUBROUTINE DET3
PURPOSE
TO COMPUTE A VECTOR OF DERIVATIVE VALUES GIVEN A VECTOR OF
FUNCTION VALUES WHOSE ENTRIES CORRESPOND TO EQUIDISTANTLY
SPACED ARGUMENT VALUES.
USAGE
CALL DET3(H,Y,Z,NDIM,IER)
DESCRIPTION OF PARAMETERS
H - CONSTANT DIFFERENCE BETWEEN SUCCESSIVE ARGUMENT
VALUES (H IS POSITIVE IF THE ARGUMENT VALUES
INCREASE AND NEGATIVE OTHERWISE)
Y - GIVEN VECTOR OF FUNCTION VALUES (DIMENSION NDIM)
Z - RESULTING VECTOR OF DERIVATIVE VALUES (DIMENSION
NDIM)
NDIM - DIMENSION OF VECTORS Y AND Z
IER - RESULTING ERROR PARAMETER
IER = -1 - NDIM IS LESS THAN 3
IER = 0 - NO ERROR
IER = 1 - H = 0
REMARKS
(1) IF IER = -1,1, THEN THERE IS NO COMPUTATION.
(2) Z CAN HAVE THE SAME STORAGE ALLOCATION AS Y. IF Y IS
DISTINCT FROM Z, THEN IT IS NOT DESTROYED.
SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
NONE
METHOD
IF X IS THE (SUPPRESSED) VECTOR OF ARGUMENT VALUES, THEN
EXCEPT AT THE ENDPOINTS X(1) AND X(NDIM), Z(I) IS THE
DERIVATIVE AT X(I) OF THE LAGRANGIAN INTERPOLATION
POLYNOMIAL OF DEGREE 2 RELEVANT TO THE 3 SUCCESSIVE POINTS
(X(I+K),Y(I+K)) K = -1,0,1. (SEE HILDEBRAND, F.B.,
INTRODUCTION TO NUMERICAL ANALYSIS, MC-GRAW-HILL, NEW YORK/
TORONTO/LONDON, 1956, PP.82-84.)