Interpolating Vertical Segments

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This Demonstration shows the polynomials of degree that interpolate a given set of vertical segments in the plane. If there is no interpolating polynomial of a particular degree, the set of all approximating polynomials of the same degree can be represented by its boundary (colored in magenta).

Contributed by: Evgenija D. Popova and Radostin Surilov (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Given a set of distinct real numbers (input data) and a set of (output) measurements that are unknown but bounded in compact real intervals . The pair is a vertical segment in the - plane We assume that the input data are in the interval with .

For a given set of vertical segments and an integer represents the set of all real algebraic polynomials of degree that interpolate the vertical segments , that is, . The set of interpolating polynomials is represented in blue; its boundary consists of piecewise real interpolating polynomials in each subinterval ; see also [2].

If, for a set of vertical segments, there is no interpolating polynomial of a particular degree, the set of all approximating polynomials of the same degree can be represented by its boundary (colored in magenta).

Details about the theory and implementation algorithms can be found in [1].

References

[1] S. M. Markov and E. D. Popova, "Linear Interpolation and Estimation Using Interval Analysis", Bounding Approaches to System Identification, New York: Plenum Press, 1996 pp. 139–157.

[2] Interval Interpolating Polynomial



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