Environmental Engineering Reference
In-Depth Information
3.1 Pad
é
Polynomials
Pad
é
approximates are a special type of rational fraction approxima-
tion to a given function. For a given power series
The Pad
é
fraction
where
and
are polynomials in
of orders
N
and
M
, re-
spectively, is used to approximate
The coefficients of
is
determined from
Eq.(4.19) indicates that the first
M + N +
1 terms of
matches
those of
and the remaining terms are negligibly small. Assume
where
M
>
N.
Substituting these results into (4.19) yields
Making use of the identity that a polynomial is zero if and only all the
coefficients of the polynomial are identically zero, we arrive at
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