Wave Propagation in Linear Media | re-examined

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6Towards a quadrature routine
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Figure 6.13: Absolute extrapolation error , log e S (k)
0
, S depending on the number of sequence mem-
bers being subject to extrapolation for WorkingPrecision->20 ( ), 30 ( ), and 40 ( ).
The conclusions of this section concerning the precision control of an automatic quadrature
routine are as follows:
The parameter that is controlled iteratively by the meta algorithm is the length of the
sequence of partial sums.
The criterion for the termination of the iteration loop is the achievement of either a
given absolute or relative error. This is the same concept that Mathematica uses for
adaptive numerical quadrature.
The default criterion must be that of the relative error. A speci cation of a minimum
absolute error must in any case be based upon a speci c knowledge of the quadrature
problem.
The working precision must be high enough that the error requirements can be met.
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