This Scientific Initiation article
covered with the aid of codes developed an
interface of the Matlab program some
comparisons between numerical approximation
methods and found which one was more
effective in certain situations. The polynomial
interpolation concepts were presented,
addressing the interpolation of Lagrange and
Newton, and segmented interpolation,
approaching cubic splines. Some applications
were developed. First, they compared the
methods Lagrange and Newton a practical
example, the determination of the width of a
river for the construction of a bridge. In another
application, it analyzed the Newton polynomial
behavior and Cubic Spline interpolation in the
Runge function. When analyzing the results, it
was concluded that between the Lagrange
interpolation and Newton latter is more efficient
since it is lighter in terms of computational
effort, but it is not suitable for situations where
it has many interpolation points ie, where the
polynomial interpolation is very high degree.
The cubic spline is efficient in these cases shows
that it uses several low degree polynomial to
form the interpolating curve.
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